The new impetus comes as Israel nervously watches Iran and its proxy force Hizbollah build a presence in neighbouring Syria, where they are fighting in support of Syrian President Bashar al-Assad. Netanyahu has accused Iran of building sites in Syria and Lebanon to produce missiles.
"Our position is straightforward. This is a bad deal. Either fix it - or cancel it. This is Israel's position," Netanyahu said in Argentina as he toured South America before travelling to New York for the UN General Assembly.
According to the agreement's sunset clause, after 10 years, Iran will be able to increase the number of centrifuges it operates beyond the current limit of 5060. The centrifuges are used to enrich uranium. Israel would like to see this time frame extended or made indefinite.
Other restrictions, including a 300kg cap on Iran's stockpile of low-enriched uranium, last 15 years.
Netanyahu has said often that as the agreement runs in its current form, it shortens the breakout time for any Iranian development of nuclear weapons. After 10 years, he has said, this breakout time will have shrunk to zero.
However, the agreement stipulates in its opening paragraph: "Iran reaffirms that under no circumstances will Iran ever seek, develop or acquire any nuclear weapons." So if Iran waited 10 or 15 years for sunset provisions to expire before building a nuclear bomb, it would still be breaking the accord.
According to the Army Radio report, Netanyahu will also ask Trump to prevent Iran from conducting research in the nuclear field and developing advanced-stage centrifuges, with much higher power.
In addition, the report said, Israel will demand that Iran cease developing long-range missiles and that a clause be added to the agreement to limit Iran's support of organisations such as Hamas and Hizbollah, which Israel and the United States consider terrorist groups.
Spokesmen for the Israeli Foreign Ministry and the prime minister's office declined to confirm whether Netanyahu would raise these issues with Trump. But Yaakov Nagel, former director of Israel's National Security Council, said in a radio interview that these demands are nothing new and are in keeping with Israel's position from the beginning of negotiations over Iran's nuclear programme.
"Israel has not changed its position," Nagel said. "Even when the agreement was signed, we said there were three or four clauses that were really bad. The deal that exists basically gives Iran the right to develop uranium."
The US President must inform Congress every 90 days about whether Iran is complying with the nuclear agreement. The next report is scheduled for October 15.
Earlier this month, the US ambassador to the United Nations, Nikki Haley, said the President has grounds to declare Iran noncompliant, raising speculation about whether he intends to keep the United States in the pact.
Trump has also slammed the agreement, which was reached two years ago between Iran on one side and the United States, Russia, China, Britain, France and Germany on the other. It gave Iran relief from nuclear-related economic sanctions in return for curbs on Tehran's nuclear programme.
In July, however, following a meeting between Trump and his senior national security advisers, his Administration told Congress that Iran has been complying with the nuclear deal.
Haley pointed to breaches in the amount of heavy water - which is used in certain kinds of nuclear reactors - that Iran was allowed to have and its refusal to open up all its sites for inspection as grounds for declaring Iran to be noncompliant.
With deep concern over North Korea's nuclear tests, there is currently an "opportunity" to send a message over the Iranian threat, said Yossi Kuperwasser, a researcher at the Jerusalem Centre for Public Affairs and a former director of the Ministry of Strategic Affairs.
"It's clear that if we don't do anything, Iran will become a new North Korea, except more dangerous," Kuperwasser said.
Speaking at a counterterrorism conference in Tel Aviv, Israeli Education Minister Naftali Bennett called on the United States to throw its full economic weight behind sanctioning Iran.
Intelligence Minister Israel Katz said the Prime Minister must demand that Trump freeze, change or cancel the agreement.
"The lesson to be learned from the Korean case is that dialogue and compromise with dictatorships seeking nuclear capability, rather than decisive action, ultimately leads to crossing the threshold and changing the rules of the game," he said.
