However, his predecessor Barack Obama argued the deal, between Iran and six world powers including China, Russia and the United Kingdom, was the best way to prevent Iran getting a nuclear weapon.
The U.S. has been exploring ways to address the threat of North Korea's nuclear program, which is significantly farther along than Iran's.
Trump has had harsh words for the Iran nuclear deal since his campaign, calling the deal "catastrophic - for America, for Israel, and for the whole Middle East" in a speech past year to the American Israel Public Affairs Committee.
And a nuclear-armed Iran could be very, very bad. Despite repeated pledges to rip up, renegotiate or otherwise alter them, the US has yet to withdraw from any of these economic, environmental or national security deals, as Trump's past criticism turns to tacit embrace of several key elements of USA foreign policy. "We buy them off for a short period of time, and then someone has to deal with it later". "We could be wrong".
Iran produced 3.77 million b/d of crude oil in March, according to the most recent S&P Global Platts OPEC survey. The secretary also said, a bit confusingly, in a public statement at the State Department yesterday, that "The JCPOA fails to achieve the objective of a non-nuclear Iran". "None of the other countries would be up for that".
North Korea said it may test missiles on a weekly basis, and warned of "all-out war" if the United States takes military action.
The Trump administration now says it is reviewing these accords.
On Iran, Trump and his top officials have been walking a narrow line as they seek to show an aggressive stance.
Appearing in the same NewsHour program, James Robbin, a former special assistant in the defense secretary's office during the George W. Bush administration, said a USA pullout from the nuclear deal would not be without precedent.
So what do you think about Donald Trump's decision on the Nuclear deal?
In a statement on Wednesday, Mr Tillerson said a review, which he had announced in a letter to Congress a day earlier, would look at the whole USA policy towards Iran - taking in not only Tehran's compliance with the nuclear deal but also its actions in the Middle East. "There would have been no way to get a deal if we lumped in everything else we don't like about Iran".
Like the diplomats, Kirby said the administration may be looking for political cover.
He noted that it was necessary for Tillerson to separate the notions of terrorism and nuclear deal, which have nothing in common.
When Spicer was questioned whether Trump was concerned Iran was cheating on the deal, he said "That's why he's asking for this review".
Reapplying sanctions would violate the terms of the deal orchestrated by former President Barack Obama alongside Russia, China and the EU.
But, Robbin, now a national security analyst with the American Foreign Policy Council, a Washington research group, said he did not foresee the Trump administration withdrawing completely from the nuclear deal.
While disparaging the nuclear deal and accusing Iran of fomenting violence and terrorism throughout the Middle East, Trump has avoided committing to abandoning the agreement, a move that would be staunchly opposed by US businesses and European allies.
Tillerson's statement went on to describe some of those provocations, including support for terrorism, interference in Iraq, backing the Assad regime in Syria, support for the Houthis in Yemen, harassment of USA navy ships in the Persian Gulf, and cyber-attacks against US interests and allies.
But Majidyar argued that scrapping the deal wouldn't help Washington.
"The evidence is clear: Iran's provocative actions threaten the United States, the region and the world", he said. "What I see is a more strict (US) interpretation of the deal and that interpretation will be different than Iran's interpretation".
The move is the latest attempt by Mr Trump to refocus his efforts on protecting American jobs and manufacturing, a key election campaign. "If he didn't, if he thought everything was fine he would've allowed this to move forward".
Earlier on Wednesday, Defense Secretary James Mattis also accused Iran of seeking to destabilize the Middle East.
He also said he thought the threshold for any US withdrawal from the JCPOA would be "quite high", given that it could have "very significant diplomatic consequences" for Washington.