In a combative speech on Friday, Mr Trump accused Iran of sponsoring terrorism and proposed new sanctions.
He said Iran had already violated the 2015 deal, which imposed curbs on Iran's nuclear capability in return for easing international embargoes.
International observers say Iran has been in full compliance with the deal.
Speaking at the White House, Mr Trump said he was acting in order to deny Iran "all paths to a nuclear weapon".
"We will not continue down a path whose predictable conclusion is more violence, more terror, and the very real threat of Iran's nuclear breakout," he said.
Congress requires the US president to certify every 90 days that Iran is upholding its part of the agreement. Mr Trump had already recertified twice, but refused to sign a third time ahead of a Sunday deadline.
Congress now has 60 days to decide whether to pull out of the nuclear deal by re-imposing sanctions.
Some advocates of the deal, signed between Iran and six international powers - the UK, US, Russia, France, Germany, and China - had feared that Mr Trump would withdraw the US entirely.
Instead he essentially passed the ball to Congress, which will now decide whether to rewrite the framework in accordance with Trump's wishes. The president made it clear that if it did not, he would cancel the deal.
"In the event we are not able to reach a solution working with Congress and our allies, then the agreement will be terminated," he said. "It is under continuous review and our participation can be cancelled by me, as president, at any time."