The deal has allowed many Western companies to resume business with Iran, including Boeing, which has signed two major agreements to deliver dozens of planes to Iran. Defense Secretary Jim Mattis said during a visit Wednesday to Saudi Arabia, "everywhere you look if there's trouble in the region, you find Iran".
But he also signaled that the USA would not immediately tear up the deal as Donald Trump repeatedly pledged on the campaign trail.
But Tillerson is leaving open the possibility that the Trump administration will uphold it anyway.
Tillerson said one of the mistakes in the way the agreement was put together was that it ignored all the other serious threats Iran posed outside of its nuclear program.
US Secretary of State Rex Tillerson raised the concerns in a letter sent to Speaker of the House of Representatives Rep. Paul Ryan (R-Wis.) Tuesday, alerting Congress to an effort led by President Donald Trump to evaluate whether the continued lifting of sanctions on Iran would be in America's national security interests.
After receiving billions in cash assets and other economic relief, Iran invested heavily in its military and the Iranian Revolutionary Guard Corps, or IRGC, which continues to meddle in Syria, Iraq, Yemen, and a host of other countries.
Trump, in a news conference with the visiting Italian premier, didn't telegraph whether he would ultimately decide to keep the U.S.in the deal or not, though he called it "terrible agreement" that was poorly negotiated.
"An unchecked Iran", Tillerson said, has the potential to take the same path as North Korea "and take the world along with it".
Tillerson is also likening Iran's behavior to that of North Korea.
The White House is aware of "potential negative impacts" from a review ordered by President Donald Trump of whether lifting sanctions through the Iran nuclear deal was in USA national security interests, his spokesman said on Wednesday.
However, Tillerson's letter was in line with many other assessments that have found Iran has kept its part of the bargain. Iran has complained that sanctions relief never gave it the economic boost it craved, and it has blamed the United States for not doing enough to allow US businesses and banks to set up shop in Iran.
Still, since taking office, Trump has stopped promising he'll gut the deal.
The nuclear deal relaxed restrictions on Iran's oil sector in exchange for concessions on its nuclear program.
"It is their habit to unsettle people and nations", Tillerson said.