The United Nations Security Council was set to meet later today after Israel requested it condemn Iran's attack and designate the Revolutionary Guards a terrorist organisation.
Iran's Fars news agency quoted a source as saying Tehran was closely watching Jordan, which might become the next target is case of any moves in support of Israel, Reuters reported.
Israel reopened its airspace this morning, its airports authority said. Jordan, which lies between Iran and Israel, had readied air defences to intercept any drone or missile that violated its territory, two regional security sources said.
Residents in several Jordanian cities said they heard heavy aerial activity.
Syria, an ally of Iran, said it was putting its ground-to-air defence systems around the capital and major bases on high alert, army sources there said.
Tehran's attacks late on Saturday, launched after a suspected Israeli air strike on its embassy compound in Damascus on April 1 that killed officers of the elite Islamic Revolutionary Guard Corps, raised the threat of a wider conflict.
Iran had relied on its proxies across the region to attack Israeli and US targets in a show of support for the Palestinian group Hamas in the Gaza war with Israel, which shows no sign of easing despite numerous mediations efforts.
The Israeli military said the armed forces had shot down more than 99 per cent of the Iranian drones and missiles and were discussing follow-up options.
Regional power Egypt urged "utmost restraint".
The Iranian salvo caused light damage to one Israeli military facility.
The Israeli military said it was not advising residents to prepare to take shelter, revising an earlier alert in an apparent signal of the end of the threat.
Tehran said its strike was punishment for "Israeli crimes". Israel has neither confirmed nor denied responsibility for the consulate attack.
"Should the Israeli regime make another mistake, Iran's response will be considerably more severe," the Iranian mission to the United Nations said, warning the US to "stay away". However, it also said Iran now "deemed the matter concluded".
US President Joe Biden, who spoke by phone with Israeli Prime Minister Benjamin Netanyahu, said he would convene a meeting of leaders of the Group of Seven major economies on Sunday to coordinate a diplomatic response to what he called Iran's brazen attack.
Its Defense Secretary Lloyd Austin said America did not seek conflict with Iran but would not hesitate to act to protect US forces and support defence of Israel.
The European Union, Britain, Japan, Czech Republic, Denmark, France, Mexico, the Netherlands and Norway condemned Iran's attack.