President Donald Trump said a US "armada" was heading toward 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, the president told reporters on 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 Thursday that the force had its "finger on the trigger."

A fortnight of protests starting in late December shook Iran's clerical leadership under supreme leader Ayatollah Ali Khamenei, but the movement has petered out in the face of a crackdown that activists say killed thousands, accompanied by an unprecedented internet blackout.

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 Thursday accused the United States and Israel of stoking the protests as a "cowardly revenge... for the defeat in the 12-Day War".

'Legitimate targets'

Guards commander General Mohammad Pakpour warned Israel and the United States "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.

Activists accuse the Guards of playing a frontline role in the deadly crackdown on protests.

The group is sanctioned as a terrorist entity by countries including Australia, Canada and the United States, and campaigners have long urged similar moves from the EU and Britain.

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

Real toll?

Giving their first official toll from the protests, Iranian authorities on Wednesday said 3,117 people were killed.

The statement from Iran's foundation for martyrs and veterans distinguished between "martyrs", members of security forces or innocent bystanders, and what it called US-backed "rioters".

It said 2,427 of the dead were "martyrs".

Pezeshkian said Thursday that protest was "the natural right of citizens" but a distinction had to be drawn between protesters whose "hands are stained with the blood of innocent people".

Rights groups say the heavy toll stems from security forces firing directly on protesters and that the actual number of dead could be far higher, even more than 20,000.

Efforts to confirm the scale of the toll have been hampered by a national internet shutdown, with monitor NetBlocks saying Thursday the blackout had surpassed "two full weeks".

"All the evidence gradually emerging from inside Iran shows that the real number of people killed in the protests is far higher than the official figure," said the director of the Iran Human Rights NGO Mahmood Amiry-Moghaddam, saying the authorities' toll has "no credibility whatsoever".

IHR says it has verified at least 3,428 deaths. 

Another NGO, US-based Human Rights Activists News Agency (HRANA), has documented 4,902 deaths.

HRANA says at least 26,541 people have been arrested. On Thursday, state TV announced more than 200 more arrests in provinces including Kermanshah in the west and Isfahan in central Iran.