Israel's international allies and aid groups have repeatedly warned against a ground incursion into refugee-packed Rafah, where Israel says four Hamas battalions are holed up. Israel says the operation is needed to root out the remaining fighters.
Fighting has intensified elsewhere across the Gaza Strip in recent days, including in the north, with the Israeli military heading back into areas where it had claimed to have dismantled Hamas months ago.
Fierce gun battles were continuing 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. We lost contact with some relatives after they were warned by the army in phone calls to leave and they refused," Nasser, 57, a father of six, told Reuters, using an international phone card.
In Rafah, which borders Egypt, Palestinian residents on Tuesday afternoon said they could see smoke billowing above eastern districts of the city and heard explosions after Israel bombarded a cluster of houses.
Hamas' armed wing, the Qassam Brigades, said it had destroyed an Israeli troop carrier with an Al-Yassin 105 missile in the eastern Al-Salam district, killing some crew members and wounding others.
The Israel Defense Forces (IDF) declined to comment on the report.
In a round-up of its activities, the IDF said its forces had eliminated "several armed terrorist" cells in close-quarter fighting on the Gazan side of the Rafah border crossing with Egypt. In the east of the city, it said it had also destroyed militant cells and a launch post from where missiles were being fired at IDF troops.
'NOWHERE IS SAFE NOW'
UN Secretary-General Antonio Guterres was appalled by Israel's escalation in and around Rafah and by Hamas' indiscriminate firing of rockets there, his spokesperson said.
"Civilians must be respected and protected at all times, in Rafah and elsewhere in Gaza. For people in Gaza, nowhere is safe now," Stephane Dujarric said, adding that Guterres again called for an immediate humanitarian ceasefire.
Israeli Foreign Minister Israel Katz said on Tuesday Egypt must be "persuaded" to reopen the Rafah border crossing to "allow the continued delivery of international humanitarian aid" into Gaza.
His comment prompted an angry response from Egypt's Foreign Minister Sameh Shoukry, who said in a statement that Israel's seizure of the Rafah crossing and its military operations in the area were the main obstacles to aid entering Gaza.
UNRWA, the main United Nations aid agency in Gaza, estimates some 450,000 people have fled Rafah since May 6.
The war has pushed much of Gaza's population to the brink of famine, the UN says, and has devastated its medical facilities, where hospitals, if working at all, are running short of fuel to power generators and other essential supplies.
The World Court, also known as the International Court of Justice (ICJ), said it would hold hearings on Thursday and Friday to discuss a request by South Africa seeking new emergency measures over the Rafah incursion, which Qatar says has stalled efforts to reach a ceasefire.
South Africa's demand is part of a case it brought against Israel accusing it of violating the genocide convention in Gaza, and which Israel has called baseless. Israel will provide its views on the latest petition on Friday, the ICJ said.
Israel issued evacuation orders for people to move from parts of eastern Rafah a week ago, with a second round of orders extending to further zones on Saturday.
They are moving to tracts of land such as Al-Mawasi, a sandy strip bordering the coast that aid agencies say lacks sanitary and other facilities to host an influx of displaced people.
DEATH TOLL SPIKES
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. It said that 82 Palestinians were killed in the past 24 hours, the highest death toll in a single day in many weeks.
Israel launched its Gaza operation following an attack on October 7 by Hamas-led gunmen who killed some 1200 people and took more than 250 hostages, according to Israeli tallies.
In the Zeitoun neighbourhood of Gaza City in the north, Israeli bulldozers demolished clusters of houses on Tuesday to make a new road for tanks to roll through into the eastern suburb.
A strike on a house in Beit Lahiya, northern Gaza, killed seven people and wounded several others, medics said.
The IDF said it had killed dozens of Hamas fighters in Jabalia and dismantled a network of explosives, while in Zeitoun it located tunnel shafts and destroyed several rocket launchers.
With fighting intensifying, Qatar's Prime Minister Sheikh Mohammed bin Abdulrahman Al-Thani said ceasefire talks, mediated by his country and Egypt, were at a stalemate.
