US President Donald Trump said an American "armada" was heading towards the Gulf and that Washington was watching Iran closely, even after downplaying the prospect of imminent military action and saying Tehran appeared interested in talks.

Trump has repeatedly left open the option of new military action against Iran after Washington backed and joined Israel's 12-day war in June aimed at degrading Iranian nuclear and ballistic missile programmes.

The prospect of immediate American action seemed to recede in recent days, with both sides insisting on giving diplomacy a chance.

On his way back from the World Economic Forum in Davos, Trump said aboard Air Force One the United States was sending a "massive fleet" toward Iran "just in case."

"We're watching Iran," he said. "I'd rather not see anything happen but we're watching them very closely."

Addressing the WEF on Thursday, Trump said the United States attacked Iranian uranium enrichment sites last year to prevent Tehran from making a nuclear weapon.

Iran denies its nuclear programme is aimed at seeking the bomb.

"Can't let that happen," Trump said, adding: "And Iran does want to talk, and we'll talk."

The commander of Iran's Revolutionary Guards had also warned Washington on Thursday that the force had its "finger on the trigger".

Last week, Trump pulled back from a threat to strike Iran over its deadly crackdown on the protests after the White House said Tehran had halted planned executions of demonstrators.

In a standoff marked by seesawing rhetoric, Trump had on Tuesday warned Iran's leaders the United States would "wipe them off the face of this Earth" if there was any attack on his life in response to a strike targeting Khamenei.

Iranian President Masoud Pezeshkian in a speech on Thursday accused the United States and Israel of stoking the protests as a "cowardly revenge... for the defeat in the 12-Day War".

Guards commander General Mohammad Pakpour warned the two countries "to avoid any miscalculations" and learn from "what they learned in the 12-day imposed war, so that they do not face a more painful and regrettable fate".

"The Islamic Revolutionary Guard Corps and dear Iran have their finger on the trigger, more prepared than ever, ready to carry out the orders and measures of the supreme commander-in-chief," he was quoted by state television on the IRGC's national day.

General Ali Abdollahi Aliabadi, head of Iran's joint command headquarters, warned that if America attacked, "all US interests, bases and centres of influence" would be "legitimate targets" for Iranian forces. (AFP)