(Reuters) - Israeli forces thrust deeper into the Jabalia camp in northern Gaza on Tuesday, laying waste to residential districts with tank and air bombardments, residents said, while Israeli air strikes killed at least five people in the southern city of Rafah.

Simultaneous Israeli assaults on the northern and southern edges of the Gaza Strip this month have caused a new exodus of hundreds of thousands of people fleeing their homes, and sharply restricted the flow of aid, raising the risk of famine.

In Jabalia, a sprawling refugee camp built for displaced civilians 75 years ago, the Israeli army used bulldozers to clear shops and property near the local market, residents said, in a military operation that began almost two weeks ago.

Israel said it has returned to the camp, where it had claimed to have dismantled Hamas months ago, to prevent the militant group that controls Gaza from rebuilding its military operations there.

The health authorities and Gaza Civil Emergency Service said dozens of bodies remained trapped under rubble of houses and on the roads in Jabalia, but rescue teams have been unable to reach them.

"Israel is destroying the camp on the heads of the people, the bombardment never stops, and the world is calling for more food to enter Gaza. We want to spare lives not extra food," said Abu El-Nasser, a resident of Jabalia, who fled to nearby Gaza City.

More than 35,000 Palestinians have been killed in the war, which is now in its eighth month, according to the Gaza health ministry. At least 10,000 others are missing and believed to be trapped under destroyed buildings, it says.

Israel is seeking to eradicate Hamas after militants from the group stormed into southern Israel on Oct. 7, killing 1,200 and taking more than 250 hostages, by Israeli tallies.

The war has devastated the overcrowded coastal enclave, destroying houses, schools and hospitals and creating a dire humanitarian crisis.

In a roundup of its military activity over the past day, the Israeli Defence Forces said they had dismantled "about 70 terror targets" throughout the Gaza Strip, including military compounds, weapon storage sites and warehouses, missile launchers and observation posts.

Residents and medical officials said Israeli tanks were besieging the Al-Awda Hospital in Jabalia for the third day, and opened fire against Kamal Adwan hospital in nearby Beit Lahiya town, medics said.

In the north, an airstrike on a house in Jabalia killed at least three people overnight. In the south, airstrikes killed three children in a house in Khan Younis and at least five people including three children in a home in Rafah.

East of Khan Younis, residents said they were fleeing Khuzaa town after Israeli troops began a limited incursion on the eastern edge of the territory, bulldozing across the border fence.

"Bombing everywhere, people are leaving in panic. It was a surprising incursion," one resident from Khuzaa told Reuters over the phone as he and his family were leaving.

Israel is pushing on with its operations in Rafah on Gaza's southern edge, where more than half of the territory's 2.3 million population had sought refuge after being displaced from areas further north.

UNRWA, the main United Nations agency in Gaza, estimated as of Monday that more 800,000 had fled since Israel began targeting the border city at the beginning of the month, despite international pleas for restraint on concern over civilian casualties.

Israel has pledged to continue with the Rafah assault to root out what it says are four remaining battalions of Hamas fighters holed up there.

The Israeli military said over the past day it had "identified a terrorist shooting mortar shells at IDF troops", though no injuries were reported. It said it had taken out the foe with an airstrike and had located rockets and additional military equipment in the area.

(Reporting by Nidal Al-Mughrabi in Cairo; writing by Sharon Singleton)

By Nidal al-Mughrabi