The defence secretary, James Mattis, said this week that staying with the deal, under which Iran accepted strict curbs on its nuclear programme in exchange for sanctions relief, was in USA national security interests.
He claimed the Iranian regime supports terrorism and exports violence and chaos across the Middle East.
Asked about whether he would "decertify" the deal, he said: "You'll be hearing about Iran very shortly".
Trump has fiercely criticized it as a one-sided deal that gives Iran all the advantages.
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He refused voluntary extradition to the USA , maintaining that, as a Russian citizen, he should be tried by a Russian court. USA prosecutors are reportedly seeking a prison sentence of more than 50 year for Levashov.
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Trump "wants to look for a broad strategy that addresses all of those problems, not just one-offing those", she said.
"Maybe it's the calm before the storm", the president replied.
The agreement was concluded in 2015, to stop Iran's nuclear program.
"You guys know what this represents?" the president asked reporters in the room.
President Trump had a cryptic message for the White House pool reporters Thursday night during a photo op with military leaders. "Could be the calm, the calm before the storm".
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The White House did not immediately respond to a Reuters request to clarify Trump's remarks.
Kicking the decision to Congress will force lawmakers to decide whether to impose fresh sanctions on Iran's nuclear ambitions but doing so will end the nuclear agreement.
His next deadline is October 15.
This nuclear deal limited Iran to abide by strict rules on its nuclear programme in exchange for sanctions relief.
In a meeting with the military leaders, Trump emphasised that Iran must not be allowed to obtain the nuclear weapons.
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