Since Iran viewed the embassy strike as equivalent to an attack on its own territory, sources say, a direct attack on Israeli soil by Iran itself rather than a proxy such as Hezbollah in Lebanon was a real possibility.

Countries including India, France and Russia have warned their citizens against travel to the region, already on edge over the war in Gaza, now in its seventh month.

US President Joe Biden said he was expecting Iran to attempt to strike Israel in the short term and pledged "ironclad" support for Washington's top regional ally despite diplomatic tensions over Israel's military conduct in Gaza. "We are devoted to the defense of Israel, we will support Israel, we will help defend Israel and Iran will not succeed," he said.

Iranian sources and diplomats from the US say Tehran has signalled to Washington that it wishes to avoid escalation and will not act hastily.

A defence official said the Pentagon was "moving additional assets to the region to bolster regional deterrence efforts and increase force protection for US forces."

Washington, which has had no diplomatic relations with Tehran since the aftermath of the 1979 Islamic revolution, also asked its allies to use their influence with Iran to urge restraint.

Iran's supreme leader, Ayatollah Ali Khamenei, had warned earlier this week that Israel "must be punished and will be punished", days after one of his advisers said Israeli embassies are "no longer safe".

The Israeli military said it had not issued fresh instructions to civilians, but that its forces were on high alert and prepared for a range of scenarios.

Iran has missiles capable of hitting Israel directly and in recent weeks, Israel has bolstered its air defences, which have intercepted thousands of rockets fired by Hamas from Gaza and by Hezbollah from Lebanon.

Tens of thousands of civilians have fled their homes on both sides of the border. The Israeli military has called back reservists in preparation for any escalation along its northern border, where it exchanges fire almost daily with Hezbollah.