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.