US President Donald Trump on Tuesday kept open the possibility of negotiating an agreement to denuclearise Iran, two days after he rattled his sabre at the nation on Twitter.

“We’ll see what happens, but we’re ready to make a real deal, not the deal that was done by the previous administration, which was a disaster,” he said during a speech to the Veterans of Foreign Wars.

Iran on Monday dismissed Trump’s angry warning that Tehran risked dire consequences “the like of which few throughout history have suffered before” if it made threats against the United States.

Trump withdrew in May from the 2015 nuclear accord designed to stop Iran from developing nuclear weapons. Tehran has said its nuclear work is just for electricity generation and other peaceful projects.

Iranian President Hassan Rouhani cautioned Trump on Sunday about pursuing hostile policies against Tehran, saying, "War with Iran is the mother of all wars." But he did not rule out peace between the two countries, which have been at odds since the 1979 Islamic Revolution.

"You are not in a position to incite the Iranian nation against Iran's security and interests," Rouhani said, in an apparent reference to reports of efforts by Washington to destabilise Iran's government.

Trump responded to Rouhani in a tweet late on Sunday, saying: 

Pompeo

US Secretary of State Mike Pompeo also launched a rhetorical assault on Iran's leaders on Sunday, comparing them to a "mafia" and promising unspecified backing for Iranians unhappy with their government.

Pompeo, in a California speech to a largely Iranian-American audience, dismissed Rouhani and Foreign Minister Javad Zarif, who negotiated a nuclear deal with the US and five other countries, as "merely polished front men for the ayatollahs' international con artistry."