In his hard-hitting speech from the White House, Trump accused Iran of violating the spirit of the landmark 2015 nuclear deal, known as the Joint Comprehensive Plan of Action.
He said that Iran has "committed multiple violations" of the nuclear deal which among other things allows Tehran to continue and advance its nuclear weapons programme.
Trump announced that he would not continue to certify the agreement to Congress, but stopped short of immediately cancelling US participation in the deal and left its fate in the hands of Congress.
A presidential certification to the Congress is must to avoid American sanctions on Iran.
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Trump said if he is "not able to reach a solution working with congress and our allies", then the "agreement will be terminated".
It is under continuous review and American participation can be cancelled by him as president at any time, Trump said.
Claiming that there are many flaws in the deal, Trump announced that he "cannot and will not" make certification under the JCPOA.
He also accused Iran of sponsoring terrorism and said he would deny the regime "all paths to a nuclear weapon".
"History has shown that the longer we ignore a threat, the more dangerous that threat becomes. We will not continue down a path whose predictable conclusion is more violence, more terror and the very real threat of Iran's nuclear breakout," Trump said.
"Iran is under the control of a fanatical regime that seized power in 1979 and forced a proud people to submit to its extremist rule. This radical regime has raided the wealth of one of the world's oldest and most vibrant nations, and spread death, destruction and chaos all around the globe, he said.
Observing that his new strategy addresses the full range of Iran's "destructive" actions, Trump said his administration will work with US allies to counter the regime's "destabilising activity" and support for terrorists' proxies in the region.
Trump also announced several major steps his administration is taking in pursuit of this strategy.
This he said begins with the long overdue step of imposing tough sanctions on Iran's Islamic Revolutionary Guard Corps.
He authorised the Treasury Department to further sanction the entire IRCG for its support for terrorism and to apply sanctions to its officials, agents and affiliates.
Trump alleged that the "saddest part" of nuclear deal for the United States is that all of the money was paid up front, which is unheard of.
"The Iranian regime has committed multiple violations of the agreement. For example, on two separate occasions, they have exceeded the limit of 130 metric tonnes of heavy water. Until recently, the Iranian regime has also failed to meet our expectations in its operation of advanced centrifuges, he said.
Iranian officials and military leaders have repeatedly claimed they will not allow inspectors onto military sites, even though the international community suspects some of those sites were part of Iran's clandestine nuclear programme, he alleged.
"On the grave matter of Iran's nuclear programme, since the signing of the nuclear agreement, the regime's dangerous aggression has only escalated. At the same time, it has received massive sanctions relief while continuing to develop its missiles programme."
Iran has also entered into lucrative business contracts with other parties to the agreement, he noted.
Trump said he is directing his administration to work closely with congress and its allies to address the deals many serious flaws so that the Iranian regime can never threaten the world with nuclear weapons.
Noting that Iran's nuclear programme is of big concern, he said but there are also many more immediate concerns that the US has with Tehrans destabilising activities in the region.
This includes their support of terrorist organisations, regional destabilising activities and their export of foreign fighters throughout the region to destabilise areas in support of other terrorist activities.
Earlier, the White House while announcing President Trump's new Iran strategy, said the US will revitalise its traditional alliances and regional partnerships as bulwarks against Iranian subversion and restore a more stable balance of power in the region.