The White House did not immediately respond to a request for comment about the President's tweet.
The White House has yet to offer a complete plan to address school violence amid the public outcry sparked by the Florida shooting, including addressing who would bear the financial cost.
Trump said in the tweet that arming educators and paying their bonuses would be "very inexpensive."
Teachers and law enforcement organisations oppose the idea, but several states are considering arming teachers.
Trump spent several days earlier last week hearing emotional pleas from parents and students, including some who survived the Parkland shooting, and others who had lost children in school shootings in Connecticut and Colorado. He also solicited input from state and local officials.
Trump and Vice-President Mike Pence have said school safety will be a top agenda item when they meet with the nation's governors this week.
Speaking with reporters earlier Friday as he was leaving the White House, Trump said that the school resource officer, Scot Peterson, was either a "coward" or "didn't react properly under pressure."
Trump also took Peterson, a Broward County sheriff's deputy, to task during his speech to the conservative gathering and later in the day at a joint news conference at the White House with visiting Australian Prime Minister Malcolm Turnbull, The Washington Post reports.
"He was tested under fire, and there wasn't a good result," Trump said of Peterson at the first event. "He was not a credit to law enforcement, that I can tell you."
Appearing later alongside Turnbull, Trump argued the advantage of arming teachers - he's suggested about 20 percent should carry concealed weapons - is that they "love their pupils."
"See, a security guard doesn't know the children, doesn't love the children," Trump said. "This man standing outside of the school the other day doesn't love the children, probably doesn't know the children."
While Trump has pledged to take several actions in response to the Parkland shootings, including strengthening background checks for purchasing guns, he has been most animated in recent days about his idea of arming teachers.
The concept is staunchly opposed by the National Education Association, the country's largest teachers' lobby, as well as by some law enforcement officers.
Trump acknowledged that the notion is controversial, and he said that even some "good people" are opposed. But he said that some skeptics are starting to agree with him that schools should be "a much harder site for attackers."
"We need a hardened site," Trump said. "It needs to be hardened. It can't be soft."
For much of Trump's address to the gathering of conservatives - which included multiple references to his 2016 campaign victory and a claim that his administration has been the most successful in history - the crowd was rollicking.
At one point, when Trump mentioned his vanquished opponent, Democrat Hillary Clinton, the audience broke into a chant of "Lock her up!"
But the hall fell silent as Trump turned to the tragedy in Parkland.
"This senseless act of mass murder has shocked our nation and broken our hearts," Trump said as he recalled meeting with "great families, great people" who had lost loved ones.
Besides pitching his idea of arming "gun-adept" teachers, Trump also advocated for more aggressive screening of people for mental illness before allowing them to buy guns - a notion he also stressed at the news conference with Turnbull.
"We want to be very powerful on background checks," Trump said. "When we're dealing [with] the mentally ill, as we were in this last case - he was a very sick person and somebody that should have been nabbed."
During the news conference, a reporter noted that Australia, in response a string of violence, launched a sweeping gun buyback program in 1996 and has not experienced a mass shooting since. Turnbull was asked if he urged Trump in an earlier meeting to consider a similar initiative.
Turnbull said that his predecessor in Australia had undertaken "some very big reforms" and relayed that semiautomatic weapons are essentially not available for purchase in his country. But he steered away from offering any advice to Trump.
"It's a completely different context historically, legally and so forth," Turnbull said. "We are very satisfied with our laws . . . . But we certainly don't presume to provide, you know, policy or political advice on that matter here."
Trump agreed that the United States and Australia are "very different countries with very different sets of problems."
But, he added: "I think we're well on the way to solving that horrible problem that happens far too often in the United States."
Trump also chided Peterson as Turnbull looked on, saying the day of the Parkland shooting "was not his finest moment, that I can tell you."
Peterson broke with widely accepted police practices put in place since the Columbine massacre in 1999.
Instead of waiting for backup or specially trained teams to arrive, officers are trained to pursue and eliminate the threat as soon as possible in an attempt to save lives.
Some officers involved in active-shooting incidents have described the horror that they or other officers felt during such moments as they pursued armed gunmen, who may be wielding more firepower than the responding officers.
When a gunman opened fire inside Pulse nightclub in Orlando, Florida, an off-duty officer working at the club exchanged shots with him. But that officer realized he was outgunned, holding only a handgun while the gunman had a rifle, so the officer retreated, police later said.
Broward County Sheriff Scott Israel criticized Peterson for his inaction, saying that he should have "killed the killer." Instead, Israel said, Peterson took up a position outside the school during the shooting and never went inside.
Peterson, who had been with the department for more than three decades, resigned Thursday after being suspended by Israel. Attempts to reach him were unsuccessful.
-AP, Washington Post
