"It was a bad agreement", said Trump, who has regularly blamed his predecessor Barack Obama for securing the landmark 2015 nuclear deal.
The Iran certification, made 90 minutes before a midnight Tuesday deadline, means Tehran will continue to enjoy relief from USA nuclear sanctions.
US President Donald Trump listens to a question during a joint news conference with Italian Prime Minister Paolo Gentiloni. "We're in a role everywhere, so I do not see that".
The certification of Iran's compliance, which must be sent to Congress every 90 days, is the first issued by the Trump administration.
Mr Tillerson said the USA is conducting a comprehensive review of its Iran policy and added that the Obama-era nuclear deal only "delays" Tehran's goal of becoming a nuclear state.
But after he took office, the United States president has not yet explicitly said he would pull out from the historic agreement. On the one hand, Trump wants to show he's being tougher than Obama toward Iran, but on the other hand, he's not yet ready to rip up the deal.
Tillerson told reporters the review, which he announced on Tuesday, would not only look at Tehran's compliance with a 2015 nuclear deal but also its behaviour in the region which he said undermined U.S. interests in Syria, Iraq, Yemen and Lebanon.
The US State Department last month announced a range of new sanctions, including 11 specifically against companies or individuals for transfers of "sensitive items" to the Iranian ballistic missile programme.
The secretary of state earlier acknowledged the Iranians had met the terms of the 2015 nuclear deal.
Tehran has warned that it would restore its nuclear activities to the pre-JCPOA level, if the U.S. fails to keep its end of the bargain.
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Iranian Ambassador Gholamali Khoshroo fired back at what he called the "unsubstantiated" US charges, saying the United States is waging a "misleading propaganda campaign" against his country. Obama and others argued it was narrowly tailored to take the most unsafe prospect - a nuclear-armed Iran - off the table. "A comprehensive Iran policy requires we address all of the threats posed by Iran, and it is clear there are many", he said.
Both Iran and Hezbollah are now fighting in support of Syrian President Bashar al Assad's forces.
Trump didn't specifically weigh in on the French election, nor would he say outright whether he supported countries staying in the EU.
He also said the U.S.is committed to a strong Europe, but didn't say directly whether he prefers that the European Union stay intact.
"I think it is part of a unsafe trend we see in the Trump presidency of adopting a very aggressive posture that's threatening more wars and more confrontations", added Jeremy Kuzmarov, professor of history at the University of Tulsa.
Weeks after he said he was moving on after a failed attempt in Congress to replace the Affordable Care Act, Trump said "there's no give-up" and predicted a proposed GOP overhaul of Obama's health care law was gaining popularity.
"I think we'll get both", he said.
At a ceremony in the Oval Office surrounded by steel executives, Mr Trump said it was a "historic day for American steel", saying his administration would "fight for American workers and American-made steel". It has repeatedly denied accusations by the West that it was ever trying to develop nuclear weapons.
US President Donald Trump (R) shakes hands with Italian Prime Minister Paolo Gentiloni at the White House in Washington, DC, April 20, 2017.