Thousands of internally displaced Gazans have been forced to move again as Israel pushed deep into the Palestinian enclave from north and south on Monday.

Israeli troops returned to the ruins of Gaza's northern edge to recapture an area where they had claimed to have defeated Hamas months ago, while at the opposite end of the enclave, tanks and troops pushed across a highway into Rafah.

With some of the most intense fighting for weeks now taking place on both the northern and southern edges of Gaza and hundreds of thousands of Palestinians stuck in a rock and hard place, aid groups warn that a humanitarian crisis could sharply worsen.

Israel described its latest return to the north, where it pulled out most of its troops five months ago, as part of a "mop-up" stage of the war to prevent fighters from returning, and said such operations had always been part of its plan.

Palestinians say the need to return to earlier battlegrounds is proof Israel's military objectives are unattainable.

In sprawling Jabalia, the biggest of Gaza's eight camps built 75 years ago to house Palestinian refugees from what is now Israel, tanks pushed toward the heart of the district.

Residents fled their houses along rubble-strewn streets carrying bags of belongings. Tank shells were landing in the center of the camp and airstrikes had destroyed clusters of houses, they said.

"We don't know where to go. We have been displaced from one place to the next ... We are running in the streets. I saw it with my own eyes. I saw the tank and the bulldozer. It is on that street," said one woman, who did not give her name.

The war was triggered by a Hamas-led incursion on southern Israel on Oct. 7 in which some 1,200 people were killed and more than 250 people taken hostage, according to Israeli tallies.

The Palestinian death toll in the war has now surpassed 35,000, according to Gaza health officials who fear many more bodies are lost under the rubble.

Dreadful

The fighting has laid waste to the coastal enclave and caused a deep humanitarian crisis, with the Gaza Health Ministry warning in a statement on Monday that the medical system is on the verge of collapse due to a shortage of fuel to power generators and ambulances.

Palestinian health officials said they had so far recovered 20 bodies of Palestinians killed in the overnight air strikes on Jabalia, while dozens were injured.

In Rafah, next to Gaza's southern border with Egypt, Israel stepped up aerial and ground bombardments on the eastern areas of the city, killing people in an airstrike on a house in the Brazil neighborhood.

Israel ordered residents out of the east of the city last week, and extended that order to central areas in recent days, sending hundreds of thousands of people, most of whom are already displaced, fleeing for new shelters.

Residents said Israeli air and ground bombardments were intensifying and tanks had cut off the main north-south Salahuddin Road that divides the eastern part of the city from the central area.

"The tanks cut the Salahuddin road east of the city, the forces are now in the southeast side, building up near the built-up area, the situation is dreadful and the sounds of explosions never stopped," said Bassam, 57, from the Shaboura neighborhood in Rafah.

"People continue to leave Rafah ... no place looks safe now and people do not want to escape at the last minute should tanks make sudden incursions and moving out becomes too late," he told Reuters via a chat app.

UNRWA, the main United Nations aid agency in Gaza, estimated that about 360,000 people had fled the southern city since the Israeli military gave its first evacuation order a week ago.

Bomb shipment on hold

The assault on Rafah has caused one of the biggest splits in generations between Israel and its main ally the United States, which put some deliveries of weapons on hold for the first time since the war began.

Washington has said Israel must not assault Rafah without a plan in place to protect civilians there, which it has yet to see.

Israeli Defense Minister Yoav Gallant's office said Monday he had briefed U.S. Secretary of State Antony Blinken on the "precise operation" in the Rafah area.

Jack Lew, the U.S. ambassador to Israel, signaled on Sunday that the Rafah incursion was still on a scale that Washington considers acceptable.

Hamas' armed wing said its fighters were engaged in gun battles with Israeli forces in one of the streets east of Rafah, and in the east of Jabalia.

In Israel, the military sounded sirens several times in areas near Gaza, warning of potential Palestinian cross-border rocket and or mortar launches.

Hamas and the armed wing of Islamic Jihad said in a joint statement that they fired mortar bombs against Israeli forces massing up inside the Rafah crossing, the sole checkpoint linking Gaza to Egypt, which Israel captured last week.