The notification came as the White House certified that Iran was complying with its commitments under the deal negotiated by former President Barack Obama, which is known as the Joint Comprehensive Plan of Action.
"Iran remains a leading state sponsor of terror through many platforms and methods," Tillerson wrote in a letter to Republican House Speaker Paul Ryan.
"President Donald J. Trump has directed a National Security Council-led interagency review of the Joint Comprehensive Plan of Action that will evaluate whether suspension of sanctions related to Iran pursuant to the JCPOA is vital to the national security interests of the United States."
The certification of Iran's compliance with the terms of the deal must be issued to Congress every 90 days. The latest notification was the first issued by the Trump administration.
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The deal placed curbs on Tehran's nuclear program in exchange for the lifting of international sanctions.
Trump has repeatedly denounced the agreement, and in a January interview with the Times of London and Bild newspaper called it "one of the worst deals ever made."
But he declined to say whether he intended to "renegotiate" the deal, as he asserted regularly during the presidential campaign.
The pact was signed in July 2015 by Iran and six major powers -- the United States, China, Russia, Britain, France and Germany.
Critics of the agreement, including Israel, have argued that when some of the terms of the deal expire in 10 and 15 years it will leave Tehran on the threshold of building a bomb.