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 militants have attacked tanks massing around Rafah in the south.
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.
"Tanks and planes are wiping out residential districts and markets, shops, restaurants, everything," Ayman Rajab, a resident of western Jabalia, said via a chat app.
"It is all happening before the one-eyed world."
Israel had said its forces cleared Jabalia 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 Islamist militants from re-grouping.
In southern Gaza bordering Egypt, thick smoke rose over Rafah, where an escalating Israeli assault has sent hundreds of thousands of people fleeing from what was one of the few remaining places of refuge.
"People are terrified and they're trying to get away," Jens Laerke, United Nations humanitarian office spokesperson, said in Geneva, adding that most were following orders to move north towards the coast but there were no safe routes or destinations.
As the fighting raged, the US military said trucks started moving aid ashore from a temporary pier, the first to reach the besieged enclave by sea in weeks.
The World Food Programme, which expects food, water, shelter and medical supplies to arrive through the floating dock, said the aid was transported to its warehouses in Deir Al Balah in central Gaza ready for distribution.
The UN earlier reiterated that truck convoys by land - disrupted by the assault on Rafah - were still the most efficient way of moving aid.
"To stave off the horrors of famine, we must use the fastest and most obvious route to reach the people of Gaza - and for that, we need access by land now," deputy UN spokesman Farhan Haq said.
Hamas demanded an end to Israel's siege and accused Washington of complicity with an Israeli policy of "starvation and blockade".
The White House said US national security adviser Jake Sullivan would visit Israel on Sunday and stress the need for a targeted offensive against Hamas militants rather than a full-scale assault on Rafah.
The Israel Defence Forces said troops killed more than 60 militants in Jabalia in recent days and located a weapons warehouse in a "divisional-level offensive".
A divisional operation would typically involve several brigades of thousands of troops each, making it one of the biggest of the war.
"The 7th Brigade's fire control centre directed dozens of air strikes, eliminated terrorists and destroyed terrorist infrastructure," the IDF said.
At least 35,303 Palestinians have now been killed, according to the enclave's health ministry, while aid agencies have warned repeatedly of widespread hunger and dire shortages of fuel and medical supplies.
Israel says it must capture Rafah to destroy Hamas and ensure the country's safety.
In the Hamas attack on October 7, 1200 people died in Israel and 253 were taken hostage, according to Israeli tallies.
About 128 hostages are still being held in Gaza.
Talks on a ceasefire have been at an impasse.
Israeli tanks and warplanes bombarded parts of Rafah on Friday, while the armed wings of Hamas and Islamic Jihad said they fired anti-tank missiles and mortars at forces massing to the east, southeast and inside the Rafah border crossing with Egypt.
UNRWA, the main UN aid agency for Palestinians, said more than 630,000 people had fled Rafah since the offensive began on May 6.
"They're moving to areas where there is no water - we've got to truck it in - and people aren't getting enough food," UNRWA director of planning Sam Rose told Reuters from Rafah on Friday.