Israel and Iran have agreed to hold off strikes for now but have both warned they would respond to any future attack.
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.
The attacks sparked fears the escalation could unleash a new full-scale Middle East conflict and were the first since a shaky ceasefire in April put five weeks of war on hold.
US President Donald Trump said on Truth Social that both sides were seeking an immediate ceasefire and expressed optimism about peace negotiations.
"Final negotiations on 'Peace' are proceeding, subject to ignorance or stupidity getting in its way," he wrote.
Israeli Prime Minister Benjamin Netanyahu declared that Israel's strikes on Iran would cease as "the fire on that front is contained".
But Mr Netanyahu asserted Israel's right to self-defence in a televised statement, warning that should Iran "make the mistake of resuming attacks against us, we will respond with full force".
"And I say this with appreciation and respect in my good conversations with my friend President Trump," he said.
Mr Netanyahu appeared to have openly defied Mr Trump with a strike in Beirut on Sunday and then retaliatory attacks against Iran.
Israel has, however, vowed to press on with its military campaign in Lebanon, announcing an evacuation warning for residents of an area in Southern Lebanon's Tyre.
That was despite a warning from Iran that "should acts of aggression and hostility continue, including in southern Lebanon, much more severe and crushing measures than before will follow".
Israeli Defence Minister Israel Katz said Israel would strike Beirut's southern suburbs in retaliation for every attack on northern Israel, adding the military would "continue to operate in Lebanon against the terrorist organisation Hezbollah".
"We categorically reject Iran's threats. Any Iranian attempt to link Lebanon and Iran and attack Israel will be met with great force, as happened yesterday," Mr Katz said.
An Israeli strike hit a vehicle in the city of Tyre, south Lebanon on Monday, Lebanese state media reported.
Hezbollah, meanwhile, said it targeted Israeli troops in Lebanon, but did not claim any attacks on Israeli territory.
Pakistani Prime Minister Shehbaz Sharif urged all parties to "exercise restraint and give peace a little more chance".
Meanwhile, Lebanese President Joseph Aoun has made a rare public appeal to the Israeli government and people, saying a military solution "will never provide you with security and safety" for the people in northern Israel.
"We are ready, we are willing, we are committed. Are you? If you are, let's sit and talk," said Mr Aoun in an interview with CNN.
He said he would not meet Israeli Prime Minister Benjamin Netanyahu before reaching an agreement to end the war, which he said would be a non-aggression pact and not a full peace deal.
Flights resume, schools reopen
Iran cancelled all flights to and from Iranian airports as military operations escalated but later reopened the airspace and removed flight restrictions.
Iraq also reopened its airspace when Iran announced it was halting its military operation against Israel.
Iraq's Civil Aviation Authority had initially announced a 72-hour closure of its airspace on Sunday evening, local time, after Iranian missile strikes on Israel.
Israel says it will reopen schools on Tuesday after they were closed because of Iranian missile strikes.
"Studies will resume … in all educational institutions throughout the country and will take place in full, in-person," Israel's education ministry wrote in a statement.
But classes in several northern communities along the Lebanese border would only be allowed to resume if they were held next to a protected space, the ministry added, due to the risk of incoming projectiles from the Iran-backed Hezbollah.
AFP/Reuters
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