US President Donald Trump on Sunday threatened Iran with bombings and secondary tariffs if Tehran did not come to an agreement with Washington over its nuclear programme.

In a telephone interview with NBC News, Trump said US and Iranian officials were talking but did not elaborate.

"If they don't make a deal, there will be bombing," Trump said. "But there's a chance that if they don't make a deal, that I will do secondary tariffs on them like I did four years ago."

Trump's language represented a sharpening of his comment a few days earlier that if Tehran refused to negotiate a new nuclear agreement, "bad, bad things are going to happen to Iran."

Western powers accuse Iran of having an clandestine agenda to develop nuclear weapons capability by enriching uranium to a high level of fissile purity, above what they say is justifiable for a civilian atomic energy programme.

Tehran says its nuclear programme is wholly for civilian energy purposes.

Trump in 2018 pulled the United States out of an agreement to relieve sanctions on Iran in return for curbs on its nuclear programme.

Now, in his second term, he has said he is open to talks on a new deal that could reduce the risk of military escalation.

Trump revealed in early March that he had sent a letter proposing such talks to Iran's supreme leader, Ayatollah Ali Khamenei.

Tehran, deeply suspicious of the US administration after Trump's withdrawal from the original nuclear deal, has refused to negotiate directly with Washington.

On Thursday, Iran's Foreign Minister Abbas Araghchi told the official IRNA news agency that he had delivered a letter responding to Trump's outreach to Oman, which has served as an intermediary in the past. (Agencies)