Palestinians line up to buy subsidised bread at a bakery in Gaza City, where hunger spreads after more than six months of war.[File,AFP]
"We also have hostages in Rafah, and we will do everything we can to bring them back home," the military spokesman told a briefing.
The 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 Hamas government media office said Israeli aircraft launched "dozens" of strikes overnight on central Gaza.
Rumors 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, despite Israel denying it was open.
An AFP journalist saw mothers holding their children's hands and families piling onto donkey carts with their luggage as they made the journey.
He insisted Iran did "not seek escalation or war".
In his briefing, Hagari said Israel was "still on high alert and assessing the situation".
G7 leaders also condemned Iran's attack and called for "restraint" on all sides, European Council President Charles Michel wrote on X after a video conference on Sunday.
"Ending the crisis in Gaza as soon as possible, notably through an immediate ceasefire, will make a difference," he said.
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 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 retaliation on Iran.
Israeli protesters rally in Tel Aviv calling for a hostage release deal.[Jack Guez ,AFP]
Attempting the journey back to northern Gaza, displaced resident Basma Salman said, "even if it (my house) was destroyed, I want to go there. I couldn't stay in the south."
"It's overcrowded. We couldn't even take a fresh breath of air there. It was completely terrible."
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, accusing Hamas of "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.