The State Department admits that Iran has so far maintained its side of the bargain it struck with world powers in 2015 to curtail its nuclear program in exchange for sanctions relief.
But Tillerson argued the accord had just been a way of "buying off" the regime and would only delay its development of a nuclear weapon that could threaten its region and the world.
"The Trump administration has no intention of passing the buck to a future administration on Iran," Tillerson told reporters.
The Joint Comprehensive Plan of Action (JCPOA) signed between Iran and world powers restricts its nuclear fuel enrichment for 10 years. Trump has between four and eight years left in office, depending on whether he wins a second term.
Tillerson said the JCPOA "fails to achieve the objective of a non-nuclear Iran" and was a product of "the same failed approach of the past that brought us to the current imminent threat we face from North Korea."
Trump's spokesman Sean Spicer said the review would be conducted by US government agencies over the next 90 days and recommendations would be presented to the president as to whether to stick by the deal.
The nuclear deal was reached in Vienna in July 2015 between Iran and Britain, China, France, Germany, Russia and the United States. It was implemented in January last year.
- 'Worst deal' -
The then US administration under president Barack Obama hailed it as a victory for diplomacy over the threat of another new war to disarm a rogue state in an already unstable region.
But US allies like Israel and Saudi Arabia were concerned the JCPOA does not shut down Iran's nuclear industry entirely nor forever, and Obama's domestic critics accused him of appeasing a terrorist state.
On the campaign trail, Trump was a strident opponent of the "worst deal ever negotiated" and many of his supporters, including some in Congress, have been lobbying to re-impose sanctions on Tehran.
Although Tillerson confirmed on Tuesday, at the end of a prior 90-day review period, that Iran is not cheating on the terms of the JCPOA, Washington has not ruled out breaking its own side of the agreement.
And even if the United States does not reimpose the nuclear sanctions that it dropped under the deal, it could impose penalties on Iran for its alleged sponsorship of armed "terrorist" movements in other countries.
"We have to look at Iran in a comprehensive way in terms of the threat it poses and all areas of the region and the world. And the JCPOA is one element of that," Tillerson said.
"So we are going to review completely the JCPOA itself... It is another example of buying off a power who has nuclear ambitions and we buy them off for a short period of time and someone has to deal with it later."