The decision followed a day of discussions, including an afternoon meeting of the president's security team.
The president wants Congress to modify a law that reviews U.S. participation in the nuclear deal to include "trigger points" that, if violated, would lead to the United States reimposing its sanctions, the official said.
At the end of that period, Congress had taken no action and the established protocol for American participation in the JCPOA continued unaltered.
"This is a last chance", he added.
Verifying that Iran is in compliance with the nuclear deal is part of it. The Trump administration and congressional leaders have sought European agreement on ways to toughen the deal, and such agreement is considered essential before USA legislation could go forward. Other nations have clearly stated that the USA can not revise the JCPOA itself.
Hailed by Obama as key to stopping Iran from building a nuclear bomb, the deal lifted economic sanctions in exchange for Tehran limiting its nuclear ambitions. But the European diplomats appear to have allies in Trump's own camp.
What does Mr Trump want to change? The resulting absence of desired modifications to the deal may prove to be frustrating to the White House.
Finally, Trump must resist the temptation to seize on the protests in Iran as an excuse for further undermining the nuclear agreement.
Boris Johnson, the British foreign secretary, who represented one of the three EU states in the meeting hosted by the European Commission took the stance that the USA must come up with a viable alternative before it can scrap the agreement.
Among Trump's demands are the elimination of sunset provisions in the agreement that will phase out many restrictions on Iran's nuclear program in coming years, and spelling out that Tehran's nuclear and ballistic-missile programs should be considered "inseparable". He said France remained dedicated to the agreement. Iran must allow "immediate inspections at all sites requested by worldwide inspectors", he said, and "sunset" provisions imposing limits on Iran's nuclear program must not expire.
In any event, the USA is likely to impose new sanctions on Iran over human right abuses and support for foreign extremist groups rather than nuclear back-sliding.
He paired Friday's concession with other, targeted sanctions on Iran for human rights abuses and ballistic missile development.
Officials had said that despite the recommendation of his entire national security staff, they weren't sure which way Trump would go.
Agence France Presse reported on Monday that Iranian officials had warned the global community to be prepared for American withdrawal, adding that the Islamic Republic was already prepared for "any scenario".
In a statement Saturday, Iran's Foreign Ministry said the Trump administration's "hostile and illegal act" in including Larijani in its sanctions list "has gone way beyond all internationally accepted behavior red lines". A spokesman for Boeing replied, "Throughout this process, we have followed the USA government's lead in all our dealings with approved Iranian airlines and we will continue to do so".