CAIRO (Reuters) - Israeli forces battled Hamas-led fighters in several areas across Gaza on Tuesday, while Palestinian health officials said at least 13 people were killed in Israeli bombardments in southern and central areas of the enclave.

In Rafah, a southern border city where Israeli forces have been operating since May, five Palestinians were killed in an air strike on a house, while in nearby Khan Younis, a man, his wife and two children were killed, they said.

In central Gaza in Nuseirat, one of the enclave's eight historic refugee camps, at least four Palestinians were killed in separate shelling and aerial strikes, medics said. Israeli tanks bombed the southern sector of Gaza City earlier on Tuesday, residents said.

The Israeli military said troops continued "intelligence-based" activities in Rafah, killing many Palestinian gunmen over the past 24 hours. It said air strikes had targeted militants, tunnels, and other Hamas military infrastructure.

It added that the Israeli air force had struck around 40 targets across the enclave, including sniping and observation posts, military structures, and buildings rigged with explosives.

The armed wings of Hamas and the Islamic Jihad said in separate statements their fighters attacked Israeli forces in several locations with anti-tank rockets and mortar fire.

Israel has vowed to eradicate Hamas after its militants carried out the worst attack in Israel's history on Oct. 7, killing 120 and taking more than 250 hostages, by Israeli tallies.

In the nine-month war, more than 38,000 Palestinians have been killed in enclave, according to Gaza's health authority, which doesn't distinguish between and combatant and non-combatant casualties, although officials say most of the dead were civilian.

Israel says it has lost 326 soldiers in Gaza and says at least a third of the Palestinian fatalities are fighters.

Efforts mediated by Egypt and Qatar to end the conflict and release the hostages, as well as Palestinians in Israeli jails, had appeared to be making some progress, negotiators had said.

TALKS PAUSED

However, the talks stalled on Saturday after three days of intense negotiations failed to produce a viable outcome, Egyptian security sources said, and after an Israeli strike targeting Hamas' top military chief, Mohammed Deif. The attack in the Khan Younis area killed more than 90 people and wounded hundreds of others, health authorities in Gaza said.

A Palestinian official close to the talks told Reuters on Tuesday that Hamas was keen not to be seen as halting the talks despite the stepped-up Israeli attacks.

"Hamas wants the war to end, not at any price. It says it has shown the flexibility needed and is pushing the mediators to get Israel to reciprocate," the official, who asked not to be named said.

He said Hamas believes Israeli Prime Minister Benjamin Netanyahu was trying to avoid a deal by adding more conditions that restrict the return of the displaced to northern Gaza and to maintain control over Rafah borders with Egypt, conditions that would not be acceptable to the group.

U.S. State Department spokesperson Matthew Miller said on Monday that two senior advisers to Netanyahu said Israel is still committed to reaching a ceasefire.

Citing a report by the United Nations Environment Programme, the U.N. Palestinian refugee agency UNRWA said in a post on X it would take 15 years to clear around 40 million tons of war rubble in Gaza. The effort would need 100+ trucks and cost over $500 million.

(Reporting by Nidal al-Mughrabi; Editing by Sharon Singleton)

By Nidal al-Mughrabi