Israel launched numerous airstrikes on Gaza overnight, according to Hamas, on Monday, asserting Tel Aviv's mission despite heightened tensions following Iran's unprecedented attack.

Despite Iran's launch of over 300 drones and missiles at Israel on Saturday, with most intercepted by the Israeli military, world powers have called for calm to prevent further escalation.

This marked Tehran's first direct assault on Israel, retaliating for a deadly strike in Damascus earlier this month amid ongoing violence against Palestinians in Gaza.

"Even amid Iran's attacks, our mission in Gaza to rescue hostages from Hamas, Iran's proxy, remains our top priority," stated Israeli military spokesperson Rear Adm. Daniel Hagari on Sunday.

As mediators set sights on a deal to halt the fighting triggered by Hamas' Oct. 7 incursion, 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.

"Hamas is still holding our hostages in Gaza," Hagari said of the roughly 130 people still held in Gaza.

"We also have hostages in Rafah, and we will do everything we can to bring them back home," the military spokesperson 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 Agence France-Presse (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."

Retaliation fears

The U.N. Security Council held an emergency meeting Sunday following the Iranian attack, where Israel pressed for new sanctions against Tehran and U.N. Secretary-General Antonio Guterres warned the region was "on the brink" of war.

"Neither the region nor the world can afford more war," the U.N. chief said.

"Now is the time to defuse and de-escalate."

Iran's U.N. envoy, Amir Saeid Iravani, insisted the Islamic Republic was exercising its "inherent right to self-defense" to respond to the April 1 strike on Tehran's consular building in Damascus, which has been widely attributed to Israel.

He insisted Iran did "not seek escalation or war."

In his briefing, Hagari said Israel was "still on high alert and assessing the situation."

G-7 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 cease-fire, will make a difference," he said.

Israel's top ally, the U.S., also urged caution and calm.

"We don't want to see this escalate," White House National Security Council spokesperson John Kirby told NBC.

After the attack, Joe Biden reaffirmed the U.S.'s "ironclad" support for Israel, but a senior U.S. official said the president had also told Israeli Prime Minister Benjamin Netanyahu that Washington would not offer military support for any retaliation on Iran.

Iranian President Ebrahim Raisi cautioned Israel on Sunday against a "reckless" retaliation, warning it would spark "a decisive and much stronger response."

Word of the impending attack prompted Israel to close schools and announce restrictions on public gatherings, with the army saying early Monday that those measures were being lifted for most of the country.

Truce deal 'on the table'

Hostilities between Israel and Iran's regional allies have flared since the outbreak of the conflict in Gaza.

Hamas' Oct. 7 incursion that sparked the fighting resulted in the deaths of around 1,200 people.

Israel's retaliatory offensive has killed at least 33,729 people in Gaza, mostly women and children, according to the territory's Hamas-run Health Ministry.

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 could not stay in the south."

"It is overcrowded. We could not 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 U.S., 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 cease-fire" 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 U.S. 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.