Thousands of Gazans are fleeing south on foot with only what they can carry after running out of food and water in the north, a United Nations agency said Wednesday, as Israel said its troops were deep inside Gaza City.

Over 70% of Gaza's population of 2.3 million have already fled their homes but the growing numbers making their way south point to an increasingly desperate situation in and around Gaza's largest city, which has come under heavy Israeli bombardment.

The war triggered by Hamas' Oct. 7 assault inside Israel has entered its second month, with an increasingly dire humanitarian situation inside the besieged Palestinian enclave and no end in sight.

Israel has said its war to end Hamas's rule will be long and difficult and that it will maintain some form of control over the coastal enclave indefinitely. Support for the war remains strong inside Israel.

About 15,000 people fled northern Gaza on Tuesday – triple the number that left Monday – according to the U.N. Office for the Coordination of Humanitarian Affairs. They are using Gaza's main north-south highway during a daily four-hour window announced by Israel.

Those fleeing include children, older people and people with disabilities, and most walked with minimal belongings, the U.N. agency said. Some say they had to cross Israeli checkpoints, where they saw people being arrested, while others held their hands in the air and raised white flags while passing Israeli tanks.

Residents reported loud explosions overnight into Wednesday across Gaza City and in its al-Shati refugee camp, which houses Palestinian families who fled from or were driven out of what is now Israel during the 1948 war surrounding its establishment.

"The bombings were heavy and close," said Mohamed Abed, who lives in Gaza City’s Sheikh Radwan neighborhood. He said residents panicked when they heard the news late Tuesday that Israeli ground forces were fighting deep inside the city.

The Israeli military claimed it killed a leading Hamas member without saying where he was killed. Hamas has denied that Israeli troops have made any significant gains or entered Gaza City. It was not possible to independently confirm battlefield claims from either side.

Israel, meanwhile, is focusing its operations on Gaza City, which was home to some 650,000 people before the conflict and where the military claims Hamas has its central command and a vast labyrinth of tunnels.

Hundreds of thousands have heeded Israeli orders to flee the north in recent weeks, even though Israel also routinely strikes targets in the south, often killing civilians.

Tens of thousands of Palestinians remain in the north, many sheltering at hospitals or U.N. schools. The north has been without running water for weeks, and the U.N. agency said the last functioning bakeries shut down Tuesday for lack of fuel, water and flour. Hospitals running low on supplies are performing surgeries – including amputations – without anesthesia, it said.

Majed Haroun, who lives in Gaza City, said women and children go door to door asking for food, while those in shelters rely on local donations. "They should allow aid for those children," he said.

Ameer Ghalban, who was pushing an older relative in a wheelchair down Gaza's main highway alongside others fleeing to the south, said the two of them had each lived off one piece of bread a day for the past three.

"The majority of people have left their land because the siege has become absolute in Gaza. We have no water, no electricity, and no flour," he said.

The situation is little better in the south, where hundreds of thousands of displaced people are packed into U.N.-run schools and other facilities. At one packed shelter, 600 people must share a single toilet, according to the U.N. office.

A month of relentless bombardment in Gaza has killed more than 10,300 Palestinians – two-thirds of them women and minors, according to the Health Ministry in the territory. More than 2,300 are believed to have been buried by strikes that in some cases have demolished entire city blocks. In comparison, Israeli casualties stand at 1,400.

The death toll on both sides is without precedent in decades of Israeli-Palestinian conflict.

Prime Minister Benjamin Netanyahu said Israel would maintain "overall security responsibility" in Gaza for an "indefinite period" after defeating Hamas.

Israel's main ally, the United States, is opposed to any reoccupation of the territory, from which Israel removed soldiers and settlers in 2005.

The U.S. has suggested that a revitalized Palestinian Authority could govern Gaza. But the internationally recognized PA, whose forces were driven out of Gaza by Hamas 16 years ago, says it would only do so as part of a solution that creates a Palestinian state in Gaza, the West Bank and east Jerusalem – territories Israel seized in the 1967 Mideast war.