Iran and Israel said on Monday they had halted attacks on each other following an appeal from U.S. President Donald Trump that they immediately "stop 'shooting'", though Tehran said it would resume strikes if Israel continued to hit Hezbollah in Lebanon.

The wave of attacks over the past 24 hours marked the most direct confrontation between Iran and Israel since an April ceasefire, threatening to wreck Washington's efforts to reach an agreement with Tehran to end their more than three-month war.

Oil prices - which had risen by as much as 5 per cent after the flurry of attacks - later pared gains when Iran's military said its first wave of strikes on Israel was over. The dollar retreated from its highest level in nearly two months.

A source briefed on the matter told Reuters that Israel had also decided to halt its attacks on Iran.

Israel struck Iranian targets after Tehran fired missiles towards Israeli territory late on Sunday. Tehran said its strikes were retaliation for Israeli attacks on strongholds of Iran-backed Hezbollah on the outskirts of Beirut.