Israeli tanks pushed deeper into Rafah on Tuesday, reaching some residential areas of the southern Gazan border city where more than a million people had sought shelter, and its forces pounded the enclave's north in some of the fiercest attacks in months.

Israel's international allies and aid groups have repeatedly warned against a ground incursion into Rafah, where many Palestinians fled and Israel says four Hamas battalions are holed up. Israel says it must root out the remaining fighters.

The White House said US national security adviser Jake Sullivan will visit Israel and Saudi Arabia this weekend. The Biden administration declined to comment on a report by Axios that Israel agreed not to expand its Rafah operation significantly before Sullivan's visit.

A US official who declined to be identified told Reuters that Israel promised not to make a major move in Rafah without advising Washington.

Israeli army battle tanks move near the border with the Gaza Strip on Monday. AFP

Israeli spokesperson Rear Admiral Daniel Hagari said in a briefing that Israeli forces had killed about 100 fighters, located 10 tunnel routes and found many weapons in Rafah since the start of the operation a week ago.

Fighting has intensified elsewhere across the Gaza Strip in recent days, including in the north, with the Israeli military returning to areas where it had claimed to have already dismantled Hamas. The clashes on Tuesday were the fiercest in months, residents and Hamas sources said.

"We are operating with determination in all three parts of the Gaza Strip. Forces from the air, land and sea are simultaneously striking terrorist targets," Hagari said, referring to the enclave's north, centre and south.

The Palestinian death toll in the war has now surpassed 35,000, according to Gaza health officials, whose figures do not differentiate between civilians and fighters. They said that 82 Palestinians were killed in the past 24 hours, the highest death toll in a single day in many weeks.

Palestinians remove a victim from the rubble following an Israeli bombardment in Nuseirat. AFP

Fierce gun battles raged late on Tuesday in northern Gaza's Jabalia, a sprawling refugee camp built for displaced Palestinians 75 years ago. "Many people are being trapped in their houses," Nasser, 57, a father of six, said by phone.

Israel killed about 80 fighters and destroyed rocket launchers and weapons manufacturing facilities in the heart of Jabalia on Tuesday, Hagari said. He said 13 Israeli soldiers were injured on Tuesday, four seriously.

In Gaza City, also in the enclave's north, an Israeli air strike on a house in the Sheikh Radwan neighbourhood killed four people and wounded several others late on Tuesday, medics said.

Reuters