US President Donald Trump met leaders of Muslim countries at the United Nations in New York on Tuesday for talks that the Emirati state news agency WAM said focused on an end to the war.
Trump, who earlier condemned moves by a string of countries to put pressure on Israel by recognising a Palestinian state, said a meeting with Israel would be next.
The Israeli government has urged the population of Gaza City to move south but many people hesitated, citing the lack of security and widespread hunger there.
"We moved to the western area near the beach, but many families didn't have the time, tanks took them by surprise," said Thaer, a 35-year-old father of one from Tel Al-Hawa.
Israeli forces, which began closing in on the city of more than a million in August, have ignored calls to stop an offensive the government says aims to destroy the last stronghold of Hamas militants whose 2023 attack on Israel and seizure of hostages triggered the war.
Medics said at least 20 people were killed and many others wounded when Israeli air strikes hit a shelter housing displaced families near a market in the middle of the city, and two other people were killed in a house nearby.
The Israeli military said it was looking into the reported attack on the shelter.
In the city's Tel Al-Hawa suburb tanks entered populated areas trapping people in their homes, while more tanks were seen stationed close to Al-Quds Hospital.
Tanks have also advanced closer to Gaza's largest hospital, Al Shifa, witnesses and Hamas media said.
On Monday, Palestinian authorities said tank shelling had damaged the Rantissi Hospital and put the nearby Al-Naser eye hospital at risk, forcing them to close.
Jordan, which runs a third hospital in the area, said it had moved it further south due to repeated bombardment.
The Israeli military said it would continue to enable the provision of medical services and functioning of healthcare facilities in Gaza and that staff and patients from Al-Naser and Rantissi had voluntarily evacuated.
Hundreds of thousands of people have fled Gaza City in northern Gaza, further south over the past few weeks, but many more remain, saying there is nowhere safe for them to go.
Seven people were killed in Nuseirat and near Rafah in Gaza's south, medics said.
There was no immediate comment from the Israeli military, which insists its attacks are aimed at ending Hamas rule of the enclave.
Israel has drawn widespread condemnation over its military conduct in Gaza, where more than 65,000 Palestinians, most of them civilians, have been killed, according to local health authorities, and famine has spread.
International frustration over the war in Gaza prompted some Israeli and US allies to recognise a Palestinian state this week.
Support for the war in Israel has also wavered, with 48 hostages, 20 of whom are believed to be alive, still held by Hamas in Gaza and 465 soldiers killed in combat.
Hamas has acknowledged the death of some of its military leaders but has not disclosed the number of its fighters killed.
The war began when Hamas stormed into Israel on October 7, 2023, killing some 1200 people, mostly civilians, and taking 251 hostages, according to Israeli tallies.
