Israeli forces have battled Hamas fighters in the narrow alleyways of Jabalia in northern Gaza in some of the fiercest engagements since they returned to the area a week ago, while in the south militants attacked tanks massing around Rafah.
Residents said Israeli armour had thrust as far as the market at the heart of Jabalia, the largest of Gaza's eight historic refugee camps, and that bulldozers were demolishing homes and shops in the path of the advance.
As fighting raged in the north and south of the territory, the US military on Friday said trucks carrying humanitarian assistance had started moving ashore from a temporary pier in Gaza on Friday morning.
"Israel's focus is Jabalia now, tanks and planes are wiping out residential districts and markets, shops, restaurants, everything. It is all happening before the one-eyed world," said Ayman Rajab, a resident of western Jabalia.
"Shame on the world. Meanwhile, the Americans are going to get us some food," Rajab, a father-of-four, told Reuters via a chat app. "We want no food, we want this war to end and then we can manage our lives on our own."
Israel had said its forces had cleared Jabilia months earlier in the Gaza war, triggered by the deadly Hamas-led attacks on southern Israel on October 7, but said last week it was returning to prevent the Islamist group re-establishing itself there.
At the World Court in the Hague, Israel asked judges to throw out a demand from South Africa for an emergency order to halt the assault on Rafah and withdraw Israeli troops from all of Gaza.
Despite seven months of near-continuous fighting, armed wings of Hamas and its ally Islamic Jihad have been able to fight up and down the Gaza Strip, using heavily fortified tunnels to stage attacks, highlighting the difficulty of achieving Israeli Prime Minister Benjamin Netanyahu's stated aim of eradicating the militant group.
At least 35,303 Palestinians have now been killed in the war, according to figures from the enclave's health ministry, while aid agencies have warned repeatedly of widespread hunger and the threat of disease.
Israel says it must complete its objective of destroying Hamas for its own safety after the deaths of 1200 people on October 7, and to free the 128 hostages still held out of 253 abducted by the militants, according to its tallies.
To achieve that, it says it must capture Rafah, Gaza's southernmost city bordering Egypt, where around half of the territory's 2.3 million people had sought shelter from the fighting further north.
Israel's operation against Rafah, which began in early May but has yet to escalate to an all-out assault, has ignited one of the biggest rifts in generations with its main ally, the United States. Washington held up a weapons shipment over fears of civilian casualties.
Israeli tanks and warplanes bombarded parts of Rafah on Friday, while the armed wings of Hamas and Islamic Jihad said they were firing anti-tank missiles and mortars at forces massing to the east, southeast and inside the Rafah border crossing with Egypt.
The UNRWA, the main UN aid agency for Palestinians, said that since the military offensive on Rafah started on May 6, more than 630,000 people have been forced to flee Rafah.
"Many have sought refuge in Deir al-Balah, which is now unbearably overcrowded with dire conditions," it added. Deir al-Balah, up the coast from Rafah to the north, is the only other city in Gaza yet to be assaulted by Israeli forces.
At the International Court of Justice, or World Court, in The Hague, where South Africa has accused Israel of violating the Genocide Convention, Israeli Justice Ministry official Gilad Noam defended the operation.
Noam said Israel was fighting a war of self-defence and that the military operation in Rafah was not aimed at civilians but at dismantling the last Hamas stronghold.
"There is a tragic war going on, but there is no genocide" in Gaza, Noam said.
The South African legal team, which set out its case for fresh emergency measures the previous day, framed the Israeli military operation as part of a genocidal plan aimed at bringing about the destruction of the Palestinian people.