Almost 60 people have been killed in new Israeli strikes in Gaza, Hamas-run health authorities have said, as residents reported heavy bombardments.
The Israeli military issued evacuation orders on Monday to people in large areas of the north, leading to further displacement.
Israeli officials are due in Washington for a new attempt at a ceasefire promoted by the Trump administration.
Salah, a 60-year-old father-of-five from Gaza City, said: "In the news we hear a ceasefire is near, on the ground we see death and we hear explosions," Reuters reported him as saying.
"Explosions never stopped; they bombed schools and homes. It felt like earthquakes."
Health authorities said 10 people were killed in Zeitoun and at least 13 were killed southwest of Gaza City.
Medics said most of those 13 were hit by gunfire, but residents reported an airstrike, too.
They also said 20 people, including women, children and a local journalist were killed in an Israeli airstrike on a beachfront cafe in Gaza City.
The IDF ordered people to head south, saying it planned to fight Hamas militants operating in northern Gaza, including in the heart of Gaza City.
Donald Trump has urged Israel and Hamas to agree a ceasefire - as the number of Palestinians killed in Gaza reached 56,500, according to the Hamas-run health ministry, which does not distinguish between civilians and combatants in its count.
"MAKE THE DEAL IN GAZA. GET THE HOSTAGES BACK!!!," he wrote on social media on Sunday.
The US president had raised expectations of a possible agreement this week, but some Palestinians were doubtful of the latest efforts to end the 20-month war that has laid waste to most of Gaza.
"Since the beginning of the war, they have been promising us something like this: release the hostages and we will stop the war," said one Palestinian, Abdel Hadi al Hour. "They did not stop the war."
An eight-week ceasefire was reached in the final days of Joe Biden's US presidency, but Israel resumed the war in March after trying to get Hamas to accept new terms on next steps.
Meanwhile, Israeli attacks in Gaza also continued on Sunday.
At least 15 people were killed when an IDF airstrike hit a house sheltering displaced people in the Jabaliya al Nazla area, according to an official in Gaza's Hamas-run health ministry.
He said women and children made up more than half the dead.
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During a visit to Israel's internal security service Shin Bet, Prime Minister Benjamin Netanyahu said the Israel-Iran war and ceasefire have opened many opportunities.
"First of all, to rescue the hostages," he said. "Of course, we will also have to solve the Gaza issue, to defeat Hamas, but I estimate that we will achieve both tasks."
The war in Gaza, which has continued for more than a year-and-a-half, began after Hamas militants launched attacks in Israel on 7 October 2023, killing 1,200 people and taking roughly 250 hostages.
Talks between Israel and Hamas have stalled over whether or not the war should end as part of any ceasefire.
Hamas official Mahmoud Merdawi accused Mr Netanyahu of stalling progress on a deal, saying the Israeli leader insists on a temporary agreement that would free just 10 of the hostages.
Omer Dostri, a spokesperson for Mr Netanyahu, said that "Hamas was the only obstacle to ending the war", without addressing Mr Merdawi's claim.
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Hamas says it is willing to free all the hostages in exchange for a full withdrawal of Israeli troops and an end to the war in Gaza.
Israel rejects that offer, saying it will agree to end the war if Hamas surrenders, disarms and goes into exile - something that the group refuses.
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