Why does the deal need to be certified?
Russian Foreign Minister Sergei Lavrov has told US Secretary of State Rex Tillerson that Iran abides by all its commitments on the Joint Comprehensive Plan of Action (JCPOA), and emphasized that all co-authors of the document must abide by it, the Russian Foreign Ministry said after a telephone conversation of the two diplomats.
Former Obama administration officials who played central roles in brokering the Iran nuclear agreement briefed congressional Democrats later Wednesday on the merits of the worldwide accord.
But Mr Trump is under pressure both at home and overseas not to scrap the deal.
European allies are warning of a split with the United States on the issue.
"The effect of what the president has done has really been to constrain our freedom of action", said Rep. Adam Schiff, Calif., the ranking Democrat of the House Intelligence Committee, "because steps we might have taken to constrain Iran's malevolent activity will now be viewed through the prism of the president's hostility to the nuclear deal".
What happens if Trump decertifies the deal?
After de-certification, the U.S. Congress will review - in a process that will take 60 days - whether it is time to re-apply U.S. sanctions on Iran that were suspended after the JCPOA was signed.
Iran has already threatened the U.S. with dire consequences if it imposes sanctions against the country. Those provisions relate to enriching uranium to levels near those needed to produce the fuel for a nuclear weapon, as well as other activities that limit Iran's atomic capabilities at various sites.
Two other USA officials, who also requested anonymity, said Trump's bellicose rhetoric on a number of fronts is troubling both many of his own aides and some of America's closest allies, a few of whom have asked US officials privately if Trump's real objective is attacking Iran's nuclear facilities. Engel, the top Democrat on the Foreign Affairs Committee, said unwinding the agreement would send a unsafe signal to allies and adversaries alike.
And if that fails, Cotton said, "We may have to impose new, even more coercive, sanctions". "Once it was entered into, once it was implemented, we want to see it enforced".
She said, "It is not a deal you can easily open and renegotiate". Those against it, like the president, argue it should last longer and also ban things like Iranian missile tests and support for militants.
The EU foreign policy chief says Washington's possible withdrawal from the Iran deal will send a message to the worldwide community that the USA is not trustworthy when it comes to deal making.
Watch Federica Mogherini's full interview with the NewsHour's Judy Woodruff on Wednesday.
Republican U.S. presidential candidate Donald Trump greets Senator Bob Corker (R-TN) at a campaign rally in Raleigh, North Carolina, U.S., July 5, 2016. That could include Iran pulling out of the deal as well and restarting uranium enrichment activities, or Iran could stay in the deal and try to drive a wedge between the US and its allies.
The Europeans seem more inclined to try to "build" on the deal in this way.
"Iran is kind of a long-term destabilizing actor in the region and so we remain concerned about their activities as well", U.S. General Joseph Votel told reporters.
But it could be hard to get both Iran and its ally, Russia, back to the table for a new round of talks.
"If we pass the message that with every change of administration in Washington or elsewhere deals are thrown away and renegotiated, no one would negotiate with any administration ever and any deal would be exposed to be renegotiated every term".
What exactly that will look like is still being determined, but it could include greater congressional oversight.