World powers have urged restraint after Iran late Saturday launched more than 300 drones and missiles at Israel, though the Israeli military has said the vast majority were intercepted, by allied countries.
"Even while under attack from Iran, we have not lost sight, not for one moment, of our critical mission in Gaza," Israeli military spokesman Daniel Hagari said late Sunday.
As mediators eye a deal to halt the fighting, fears grew over Israeli plans to send troops into Rafah, a far-southern city where the majority of Gaza's 2.4 million people have taken refuge.
The occupation army said it was "calling up approximately two reserve brigades for operational activities on the Gazan front", about a week after withdrawing most ground troops from the territory.
The Palestinian government media office in Gaza said Israeli aircraft launched "dozens" of strikes overnight on central Gaza.
Rumours of a reopened Israeli checkpoint on the coastal road from the besieged territory's south to Gaza City sent thousands of Palestinians heading north on Sunday.
An AFP journalist saw mothers holding their children's hands and families piling onto donkey carts with their luggage as they made the journey.
Hoping to reunite with his wife who has been in the southern city of Khan Younis, Palestinian man Mahmoud Awdeh said, "she told me over the phone that people are leaving... she's waiting at the checkpoint until the army agrees to let her head to the north".
The Israeli army however told AFP that reports the route was open were "not true".
Retaliation fears
The UN Security Council held an emergency meeting Sunday following the Iranian attack, where Israel pressed for new sanctions against Tehran and Secretary-General Antonio Guterres warned the region was "on the brink" of war.
"Neither the region nor the world can afford more war," the UN chief said.
"Now is the time to defuse and de-escalate."
Iran's UN envoy, Amir Saeid Iravani, insisted his country was exercising its "inherent right to self-defence" to respond to the April 1 Israeli strike on Terhan's consular building in Damascus.
He insisted Iran did "not seek escalation or war".
Iravani told Sky News Israel "would know what our second retaliation would be... they understand the next one will be most decisive".
Israel's war cabinet met on Sunday to discuss possible retaliation against Iran, with the country's broadcaster Channel 12 quoting an unnamed official as vowing a "significant response".
Iravani described this promise as "a threat, not an action".
But he said he believed a conclusion had been reached, adding: "I think there should be no military response from Israel."
G7 leaders also called for "restraint" on all sides.
"Ending the crisis in Gaza as soon as possible, notably through an immediate ceasefire, will make a difference," European Council President Charles Michel wrote on X after a video conference on Sunday
Israel's top ally the United States also urged caution and calm.
"We don't want to see this escalate," White House National Security Council spokesman John Kirby told NBC.
After the retaliatory attack, Joe Biden reaffirmed the United States' "ironclad" support for Israel, but a senior US official said the president had also told Israeli Prime Minister Benjamin Netanyahu that Washington would not offer military support for any attack on Iran.
Iranian President Ebrahim Raisi on Sunday cautioned Israel against a "reckless" action, warning it would spark "a decisive and much stronger response".
Truce deal 'on the table'
Late Saturday, Hamas said it had submitted its response to a truce plan presented by US, Qatari and Egyptian mediators at talks that started in Cairo on April 7.
Hamas said it was sticking to its previous demands, insisting on "a permanent ceasefire" and the withdrawal of the Israeli army.
Israel's Mossad spy agency called this a rejection of the proposal, claiming that Hamas is "continuing to exploit the tension with Iran" and aiming for "a general escalation in the region".
But the United States said mediation efforts continue.
"We're not considering diplomacy dead there," said the National Security Council's Kirby.
"There's a new deal on the table... It is a good deal" that would see some hostages released, fighting halted and more humanitarian relief into Gaza, Kirby said.
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