But for now he would hold off on recommending that Congress reimpose sanctions on Iran that would abrogate the agreement, said four people familiar with aspects of the president's thinking.
Donald Trump says he is considering "decertifying" a landmark nuclear deal brokered with Iran during the Obama administration, because Iran is "not living up to the spirit" of the agreement.
Trump spoke more generally about national security issues facing the USA before the briefing.
"We must not allow Iran.to obtain nuclear weapons", Trump said.
Trump on Thursday criticised Iran's behaviour with regard to the 2015 pact.
Trump has repeatedly lambasted the Joint Comprehensive Plan of Action (JCPOA) - one of the most important foreign policy legacies of his predecessor, Barack Obama - most recently at the United Nations general assembly last month. Tehran is now suspended under the agreement. For weeks, Trump has been promising to respond to any North Korean aggression toward the United States. Every other country involved has no desire to renegotiate the deal, so there's no way for Trump to "fix it".
Supporters say, the collapsed deal might trigger regional arms race and ruin Middle East tensions.
The EU will continue to push for the implementation of the global nuclear deal with Iran "by all sides", EU foreign policy chief Federica Mogherini said on Friday.
Jim Mattis, Trump's defense secretary, addressed the Senate on October 3. In exchange, the USA and its allies would lift numerous sanctions that have wrecked the Iranian economy.
The president is facing an October 15 deadline to certify that Iran is in compliance with the accord.
"European countries would do their utmost to preserve it", a senior European Union diplomat added. Trump said after journalists gathered in the White House state dining room to photograph him and first lady Melania Trump with the uniformed military leaders and their spouses. "We seek to bring about a change in the Iranian regime's behavior".