Israel on Tuesday bombed areas of southern Gaza where it had told Palestinians to flee to ahead of an expected invasion, killing dozens of people.

Meanwhile, mediators struggled to break a deadlock over delivering aid to millions of increasingly desperate civilians in the territory, which has been besieged and under assault by Israel since a brutal attack by Hamas militants.

Flaring violence along Israel's border with Lebanon also led to concerns over a widening regional conflict that diplomats were working to prevent.

In Gaza, people wounded in the airstrikes were rushed to the hospital after heavy attacks outside the southern Gaza cities of Rafah and Khan Younis, residents reported. Basem Naim, a senior Hamas official and former health minister, reported 27 people were killed in Rafah and 30 in Khan Younis.

An Associated Press reporter saw around 50 bodies brought to Nasser Hospital in Khan Younis. Family members came to claim the bodies, wrapped in white bedsheets, some soaked in blood.

An airstrike in Deir al Balah reduced a house to rubble, killing nine members of the family living there. Three members of another family that had evacuated from Gaza City were killed in a neighbouring home. The dead included one man and 11 women and children. Witnesses said there was no warning before the strike.

The Israeli military said it was targeting Hamas hideouts, infrastructure and command centers.

“When we see a target, when we see something moving that is Hamas, we'll take care of it. We'll handle it," said Lt Col Richard Hecht, an Israeli military spokesman.

Israel has sealed off and bombed Hamas-ruled Gaza since the militant attack on southern Israel Oct. 7 killed over 1,400 people, mostly civilians, and left about 200 captive in Gaza.

Israeli strikes have killed at least 2,778 people and wounded 9,700 others in Gaza, according to the Health Ministry. Nearly two-thirds of the dead were children, said Medhat Abbas, a Gaza Health Ministry official. The strikes have not stopped Hamas militants from continuing to barrage Israel with rockets launched from Gaza.

Another 1,200 people across Gaza are believed buried under the rubble, alive or dead, health authorities said. Emergency teams struggled to rescue people while cut off from the internet and mobile networks, running out of fuel and exposed to unceasing airstrikes.

On Monday Israeli warplanes struck the headquarters of the Civil Defence in Gaza City, killing seven paramedics. Another 10 medics and doctors have been killed on the job, health authorities said.

Israel has massed troops at the border for an expected ground offensive, but Hecht said Tuesday no concrete decisions have been made.

"These plans are being developed. They will be decided by, and presented to, our political leadership," he said.

Airstrikes, dwindling supplies, and Israel's mass evacuation order for the north of the Gaza Strip has thrown the tiny territory's 2.3 million people into upheaval and desperation.

More than 1 million Palestinians have fled their homes, and 60% are now in the approximately 14-kilometre (8-mile) long area south of the evacuation zone, the UN said.

Aid workers warned that the territory was near complete collapse as hospitals were on the verge of losing electricity, threatening the lives of thousands of patients, and hundreds of thousands of people searched for bread and water.

Some departments in Gaza's only specialised cancer hospital stopped working because of fuel shortages and the remaining wards will run out within two days, according to a statement from Sobhi Skik, director general of the Turkish Friendship Hospital.

At the Rafah crossing, Gaza's only connection to Egypt, truckloads of aid were waiting to go into the tiny, densely populated territory, and trapped civilians with foreign citizenship — many of them Palestinians with dual nationalities — were hoping desperately to get out.

Mediators were trying to reach a cease-fire to open the border, which shut down last week after Israeli airstrikes. An agreement appeared to have been reached Monday, but Israel denied reports of a cease-fire in Rafah, which would be needed to open the gates. On Tuesday morning, they were still closed.

An Egyptian official said Tuesday that Egypt and Israel agreed that the aid convoys at the border would travel into Israel for inspection at the Kerem Shalom crossing between Gaza and Israel.

The aid would then be allowed into Gaza. A brief humanitarian cease-fire would take place and foreign nationals would be allowed to exit Gaza via Rafah, the official said, speaking on condition of anonymity because he was not allowed to speak with the media.

Both Hamas and Israel cast doubt on an immediate opening.

"The crossings are closed, and I'm not aware of a truce or stop of hostilities," Hecht said.

Wael Abu Omar, Hamas' spokesman for the Rafah crossing, said: "Up until now, there is no agreement."

The World Food Programme said it had more than 300 tons of food waiting to cross into Gaza. "No one is giving up on the hope that this (crossing) would be open," said WFP official Abeer Etefa.

US Secretary of State Antony Blinken, who visited Israel for the second time in a week on Monday after a six-country tour through Arab nations, said in Tel Aviv that the US and Israel had agreed to develop a plan to enable humanitarian aid to reach civilians in Gaza. There were few details, but the plan would include “the possibility of creating areas to help keep civilians out of harm's way”.

Gen Erik Kurilla, the head of US Central Command, arrived in Tel Aviv for meetings with Israeli military authorities ahead of a Biden visit planned for Wednesday to signal White House support for Israel. Biden will also travel to Jordan to meet with Arab leaders amid fears the fighting could expand into a broader regional conflict.

Israel evacuated towns near its northern border with Lebanon, where the military has exchanged fire repeatedly with the Iranian-backed Hezbollah group.

The military said it killed four militants wearing explosive vests who were attempting to cross into the country from Lebanon on Tuesday morning. Video from a reconnaissance drone the army shared showed the militants near the border wall before they were targeted, causing an explosion. No group immediately claimed responsibility.

“Whoever approaches the border with Lebanon will be killed,” said Israeli military spokesman Rear Adm Daniel Hagari.

Israel has warned Lebanon it will strongly retaliate against attacks from across the border.

Israel fought a vicious month-long war with Hezbollah in 2006 that ended in a stalemate and a tense detente between the two sides.

Iran's Supreme Leader Ayatollah Ali Khamenei warned that Israel's continuing offensive in Gaza could cause a violent reaction across the region.

“Bombardments should be immediately stopped. Muslim nations are angry,” Khamenei said, according to state media.

Speaking to the Israeli Knesset on Monday, Prime Minister Benjamin Netanyahu warned Iran and Hezbollah, “Don't test us in the north. Don't make the mistake of the past. Today, the price you will pay will be far heavier."

Soon after he spoke, the Knesset floor was evacuated as rockets headed toward Jerusalem. Sirens in Tel Aviv prompted US and Israeli officials to take shelter in a bunker, officials said.

The Israeli military said Monday at least 199 hostages were taken into Gaza, more than previously estimated. Hamas said it was holding 200 to 250 hostages.

Hamas' military wing released a hostage video showing a dazed woman having her arm wrapped with bandages. The woman, who identified herself as Mia Schem, 21, rocked slightly as she spoke, the sound of explosions reverberating in the background.

The plight of the hostages has dominated the Israeli media since the attack, with interviews with their relatives playing on television almost constantly. Israeli officials have vowed to maintain the siege of Gaza until the hostages are released.

In Gaza, more than 400,000 displaced people in the south crowded into schools and other facilities of the UN agency for Palestinians. The agency said it has only 1 litre of water a day for each of its staff members trapped in the territory.

Israel opened a water line into the south for three hours that benefitted only 14 per cent of Gaza's population, the UN said.