He added the country would continue developing its nuclear programme and conduct its next nuclear test whenever its leaders see fit.
In the past week Trump has shown his willingness to launch military strikes, with US missiles deployed in Syria and Afghanistan.
In other developments, as tensions heighten in the Korean peninsula:
• The North Korean Foreign Ministry's Institute for Disarmament and Peace warned a thermonuclear war could break out at any moment.
• China's foreign minister Wang Yi said anyone who provokes conflict would "pay the price", and said there would be "no winners". China warned war could break out "at any moment".
• Air China announced that flights between Beijing and Pyongyang will be suspended from Monday.
• The Kremlin voiced concern about the escalation of tensions, and called for "restraint" from all parties.
• The Korean People's Army in North Korea threatened to "pulverise" US military bases in South Korea, and the South Korean presidential Blue House.
• North Korea cited US-South Korean war games, the deployment of a US aircraft carrier to the peninsula last weekend, as well as Trump's recent tweets as the cause of the threat of war.
• South Korea's Foreign Ministry said saying Han's remarks reveal the "true colours of North Korea's government that is bellicose and a breaker of regulations".
• Japan said it is maintaining high levels of surveillance and taking "every possible measure" to respond to any contingency on the Korean peninsula.
North Korea's military said it would "ruthlessly ravage" the US if Washington chose to attack.
The Korean People's Army statement boasted that US military bases in the South "as well as the headquarters of evils such as the (South Korean presidential) Blue House would be pulverised within a few minutes".
Han's earlier comments come as tensions rise over the possibility Kim Jong-un's regime will launch another nuclear weapons test tomorrow as North Korea marks the national holiday Day of the Sun, commemorating the birth of the country's founding father Kim Il Sung.
At the same time, a spokesman for the North Korean Foreign Ministry's Institute for Disarmament and Peace issued a statement condemning the United States for attacking Syria last week, while also calling for "peace by strength".
"The US introduces into the Korean peninsula, the world's biggest hotspot, huge nuclear strategic assets, seriously threatening peace and security of the peninsula and pushing the situation there to the brink of a war," the North's KCNA news agency said on Friday, citing the statement.
"This has created a dangerous situation in which a thermonuclear war may break out any moment on the peninsula and posed serious threat to the world peace and security, to say nothing of those in Northeast Asia," it said.
In a statement, the North Korean military, quoted by state media agency KCNA, said: "Our toughest counteraction against the US and its vassal forces will be taken in such a merciless manner as not to allow the aggressors to survive."
The statements were criticised by South Korea's Foreign Ministry.
It said North Korea will face strong punishment it will find hard to withstand if it makes a significant provocation, such as another nuclear test or an intercontinental ballistic missile launch.
China immediately responded, saying anyone provoking conflict will "pay the price".
China's foreign minister Wang Yi said today there would be "no winner" in any war, as tensions mount with the US.
He told reporters in Beijing: "Dialogue is the only possible solution." Wang stated: "Lately, tensions have risen with the US and the ROK (Republic of Korea in the South) on one side, and the DPRK (Democratic People's Republic of Korea in the North) on the other, and one has the feeling that a conflict could break out at any moment.
"If a war occurs, the result is a situation in which everybody loses and there can be no winner."
Wang said that whichever side provoked a conflict "must assume the historic responsibility and pay the corresponding price".
Kremlin spokesman Dmitry Peskov told journalists: "Moscow is watching with great concern the escalation of tensions on the Korean peninsula. We call for restraint from all countries and warn countries not to pursue actions that could consist of any provocative steps."
North Korea blames Trump and the US for the rising tensions, according to Han, who cited US-South Korean war games, the deployment of a US aircraft carrier to the peninsula last weekend, as well as Trump's recent tweets on Tuesday that the North is "looking for trouble".
Han's remarks, on the eve of the country's biggest national holiday, the "Day of the Sun", were released hours after a member of the Trump administration denied a report claiming the US was prepared to launch a pre-emptive strike to halt any nuclear test at the weekend.
He ordered air strikes on a Syrian air base in response to a chemical weapon attack and yesterday dropped the "mother of all bombs" on a network of caves in Afghanistan, killing 36 ISIS fighters.
In another show of force, US military planes have been conducting military drills alongside Japan in the Korean peninsula.
On Tuesday the US President tweeted: "North Korea is looking for trouble. If China decides to help, that would be great. If not, we will solve the problem without them! U.S.A."
Trump also called North Korea a "menace" earlier this week and tweeted that if China doesn't do its part to rein in Pyongyang's nuclear ambitions, the US "will solve the problem without them".
Han said: "As long as the nuclear threats and blackmail go on with the military exercises, we will carry forward with our national defense buildup, the core of which is the nuclear arms buildup."
He also talked of a sixth nuclear test, saying: "That is something that our headquarters decides. At a time and at a place where the headquarters deems necessary, it will take place."
The North Korean official dismissed the suggestion Trump made last year during his presidential campaign that he was willing to meet Kim, possibly over hamburgers.
"I think that was nothing more than lip service during the campaign to make himself more popular," Han said.
"Now we are comparing Trump's policy toward the DPRK with the former administration's and we have concluded that it's becoming more vicious and more aggressive."
US Vice President Mike Pence will embark on a 10-day visit to Asia, starting in South Korea on Sunday with contingency plans should it coincide with a nuclear test, a White House adviser said.
CIA director Mike Pompeo said North Korea was closer now than it had ever been to being able to threaten the US with a nuclear-tipped intercontinental missile and increased its technical know-how with each new test.
Experts do not believe North Korea has a deliverable long-range nuclear weapon, or intercontinental missiles.
But that could change within the next few years, as experts say North Korea could have a viable nuclear warhead and a ballistic missile capable of hitting the US mainland during Trump's watch as president.
Aerial photos taken Tuesday show continued activity at the Punggye-ri Nuclear site where US officials fear a nuclear device has been installed in a tunnel ahead of another test.
And Han, referring to North Korea as the Democratic People's Republic of Korea, said Friday: "If the US comes with reckless military manoeuvres then we will confront it with the DPRK's pre-emptive strike.
"We've got a powerful nuclear deterrent already in our hands, and we certainly will not keep our arms crossed in the face of a US pre-emptive strike."
The message had been echoed in the days before, when North Korea said it would launch a "merciless retaliatory strike" against US military action.
Pyongyang also recently launched a ballistic missile and some experts say it could conduct another nuclear test at virtually anytime.
But North Korea blames Trump and the US for the rising tensions, according to Han.
"Trump is always making provocations with his aggressive words. So that's why. It's not the DPRK but the US and Trump that makes trouble," he said.
The annual military exercises have consistently infuriated the North, which views them as rehearsals for an invasion.
Washington and Seoul deny that, but reports that exercises have included "decapitation strikes" aimed at the North's leadership have fanned Pyongyang's anger.
"Our stance toward their hostile policy is strident and clear-cut," Han said. "Now the Trump administration is thinking about several options as regards the DPRK. Those options include such reckless options as headquarter decapitation and the pre-emptive strike.
"Whatever comes from the US, we will cope with it. We are fully prepared to handle it."
US intelligence officials told NBC if the US is convinced North Korea will follow through on a test, it can pre-emptively deploy Tomahawk missiles from two war ships parked in the region.
Bombers are also being lined up in Guam, and cyber and special operations on the ground may be utilised, the officials said.
But a member of the administration shot down the idea, describing the report as "flat wrong", while another official told Reuters it was "speculative at best".
The Pentagon declined comment, saying, as a policy, it does not discuss future operations "nor publicly speculate on possible scenarios".
Pence will travel to South Korea on Sunday in what his aides said was a sign of the US commitment to its ally.
His Seoul stop kicks off a long-planned 10-day trip to Asia - his first as vice president - and comes amid concerns that Pyongyang could soon conduct its sixth nuclear test.
Trump has warned against further provocations, sending an aircraft carrier group to the region as a show of force. His officials have been assessing tougher economic sanctions as well as military options to curb North Korea's nuclear ambitions.
Pence plans to celebrate Easter with US and Korean troops on Sunday before talks on Monday with acting President Hwang Kyo-ahn.
"We're going to consult with the Republic of Korea on North Korea's efforts to advance its ballistic missile and its nuclear programme," a White House foreign policy adviser told reporters, previewing Pence's trip.
Pence will land in Seoul the day after North Korea's biggest national day, the "Day of the Sun".
The White House has contingency plans for Pence's trip should it coincide with a another North Korean nuclear test by its leader Kim Jong Un, the adviser said.
"Unfortunately, it's not a new surprise for us. He continues to develop this programme, he continues to launch missiles into the Sea of Japan," the adviser said.
"With the regime it's not a matter of if - it's when. We are well prepared to counter that," the adviser said.
US officials have played down the prospect of any military strike against North Korea, which would likely provoke massive North Korean retaliation and huge casualties in Japan and South Korea and among US forces in both countries.
China, North Korea's sole major ally and neighbour, opposes its weapons programme and has called for talks leading to a peaceful resolution and the denuclearisation of the peninsula.
"Military force cannot resolve the issue," Chinese Foreign Minister Wang Yi told reporters in Beijing. "Amid tensions we will also find a kind of opportunity to return to talks."
Japanese Prime Minister Shinzo Abe also underscored fears about possible threats from North Korea, telling parliament in Tokyo that Pyongyang could have the capacity to deliver missiles equipped with sarin nerve gas.
Kim Jong-un made a public appearance in Pyongyang on Thursday, to open a housing project featuring residential tower blocks of various shapes - round, square and octagonal - with the tallest proclaimed as 70 storeys, or 234m, high, and including nearly 5000 apartments in total.
About 200 foreign journalists are in Pyongyang as the country marks the 105th anniversary of "Day of the Sun".
Officials had given no details as to the nature of a planned "big" event today or where it would take place, and similar announcements in the past have been linked to relatively low-key set pieces. In the end, it turned out to be the grand unveiling of a block of flats.
In 2016, for example, foreign journalists underwent hours of investigation by North Korean officials ahead of what turned out to be a pop concert to mark the finale of a ruling Workers' Party congress.
Washington-based 38 North, who monitors North Korea, has reported "unusually high levels of activity" at the Punggye-ri Nuclear Test Site over the past four weeks.
New satellite imagery from April 2 showed there was more activity around the North Portal, which is the tunnel where the four most recent nuclear tests have taken place.
It was revealed that Kim Jong-Un had overseen a special forces commando operation, watching from an observation post as special forces dropped from light transport planes "like hail" and "mercilessly blew up enemy targets".
With a broad smile on his face, Kim praised his troops for their precision, saying "the bullets seemed to have their own eye", CNA said without identifying when the operation was held.
The Rodong Sinmun - the official mouthpiece of the ruling Workers' Party - carried several photos from the contest including one of Kim watching the troops parachuting down from jets into an open field. Another showed him grinning from ear-to-ear as he walked by cheering soldiers.
