"In what we heard yesterday, I don't see any invitation for Iran to enter dialogue", he said.
Iranian Foreign Minister Mohammad Javad Zarif responded on Twitter that the deal was not renegotiable and that Trump's stance "amounts to desperate attempts to undermine a solid multilateral agreement".
During that four-month period, he wants Congress and America's main European allies to draw up a new deal - without negotiating with Tehran - to replace the "disastrous flaws" in the current agreement.
Britain, France and Germany had called on Trump on Thursday to uphold the pact.
They were imposed on 14 Iranian entities and individuals, the most prominent of whom is the head of the country's judiciary, Sadegh Amoli Larijani.
Russian Federation on Saturday said Washington would be making a grave mistake by pulling out of the Iran nuclear deal, adding that Moscow would work hard to keep the landmark agreement alive.
Trump said on Friday he would waive nuclear sanctions on Iran for the last time to give the United States and European allies a final chance to amend the pact.
Russian Federation - one of the parties to the Iran pact alongside the United States, China, France, Britain, Germany and the European Union - called Trump's comments "extremely negative". Trump is also waiving other USA penalties covered by the agreement, including on Iran's oil and gas sectors, which were up for renewal next week.
"If at any time I judge that such an agreement is not within reach, I will withdraw from the deal immediately", he added.
The Republican leader grudgingly agreed to sign sanctions waivers, ensuring Washington will live up to its commitments for another 120 days, but he cautioned it would be "for the last time".
But Trump argues that Obama gave away too much to Iran in sanctions relief, without forcing the Islamic republic to end its ballistic missile program and support for militant groups.
In his statement Friday, Trump said he remained open to revising the Iran Nuclear Agreement Review Act, or INARA. It said the sanctions are against worldwide law and go against US commitments, saying they would bring a "strong reaction" from Iran.
Iran has said it will not accept any changes to the terms of the 2015 nuclear deal, which eased sanctions on the country in exchange for Tehran halting uranium enrichment.