Iran's President Hassan Rouhani has said the US "faces defeat" in its move to reimpose UN sanctions on the country as European allies called the unilateral declaration legally void.
In a televised speech, Mr Rouhani said Iran would "give a crushing response to America's bullying".
The Trump administration said the measures were being reimposed under the mechanism of a deal the US has quit.
The UK, France and Germany said the US had no power to carry out such a move.
The three countries - alongside China, Russia and the US - were parties of a landmark deal signed with Iran in 2015 to curb its nuclear programme.
But President Donald Trump, a critic of the Obama-era accord, withdrew the US from it in 2018.
As a result, Iran began breaching some commitments it had made, including enriching more uranium than it should.
The US said the country should be punished, declaring that all UN sanctions that had been suspended would be reimposed - a mechanism agreed in the deal called "snapback" - and that a conventional arms embargo on Iran would no longer expire on 18 October.
But Washington's announcement has been dismissed by virtually every member of the UN Security Council, and the body has not taken the measure any further. The impact of the decision remains unclear.
On Sunday, an unnamed senior US official quoted by Reuters said that from Monday, Washington would impose sanctions on more than two dozen people and entities involved in the Iranian nuclear, missile and conventional arms programmes.
How has Iran reacted?
In his speech, Mr Rouhani added: "America is approaching a certain defeat in its sanctions move... It faced defeat and a negative response from the international community."
Earlier, Iran's foreign ministry described the US efforts as "futile", saying that the "US approach is a major threat to the international peace and security and an unprecedented threat to the UN and the Security Council".
"Iran emphasizes that if the US, directly or with the co-operation of a number of its allies, makes any move in line with these threats, it will face a serious reaction and should account for all its dangerous consequences," it said in a statement, without elaborating.
How has the world reacted?
The UK and France, two permanent members of the UN Security Council, as well as Germany, said Washington's announcement was "incapable of having any legal effect" as the US used a mechanism of the deal that it had abandoned.
"It flows from this that any decisions and actions which would be taken based on this procedure or on its possible outcome would also be incapable of having any legal effect," they said in a joint statement. "We have worked tirelessly to preserve the nuclear agreement and remain committed to do so."
The foreign ministry in Russia, another permanent member of the Security Council, said: "The illegitimate initiatives and actions of the United States by definition cannot have international legal consequences for other countries."
On Saturday, UN Secretary-General António Guterres told the Security Council he could not take any action because "there would appear to be uncertainty" on the issue. But US officials argue that, despite having abandoned the agreement, they still have the right to trigger the "snapback" clause.
The announcement was made 30 days after US Secretary of State Mike Pompeo notified the council that the administration was triggering the mechanism.
In a statement late on Saturday, Mr Pompeo said measures would be announced in the coming days against countries not enforcing the sanctions, without giving details.
After abandoning the deal, the US unilaterally reinstated sanctions on Iran which, combined with a drop in oil prices, have crippled the economy in the country, which has also been hit hard by the Covid-19 pandemic.
The announcement comes around six weeks before the US presidential election. Mr Trump faces Democratic rival Joe Biden who has pledged to bring the US back to the deal.