Residents said Israeli forces bombed Gaza City from the air on Monday and blew up armoured vehicles in its streets.
Hamas said it was studying the latest US ceasefire proposal, delivered on Sunday with a warning from Trump's that it was the militant group's "last chance".
"A mighty hurricane will hit the skies of Gaza City today, and the roofs of the terror towers will shake," Israeli Defence Minister Israel Katz wrote on X.
"This is a final warning to the murderers and rapists of Hamas in Gaza and in the luxury hotels abroad: release the hostages and lay down your weapons - or Gaza will be destroyed, and you will be annihilated," he wrote.
Katz's post appeared before reports of shooting at a bus stop in Jerusalem that killed five people. Hamas praised the attackers.
According to a senior Israeli official, the latest US proposal for Gaza calls for Hamas to return all 48 remaining living and dead hostages on the first day of a ceasefire, during which negotiations would be held to end the war.
Hamas has long said it intended to hold on to at least some hostages until negotiations were complete.
It said in a statement it was committed to releasing all hostages with a "clear announcement of an end to the war" and withdrawal of Israeli forces from Gaza.
Israel launched a major assault in August on Gaza City, where hundreds of thousands of residents are living in the ruins having returned after the most intense fighting of the war's early weeks nearly two years ago.
Residents of Gaza City said Israeli forces pounded several districts from the air and ground, and detonated decommissioned armoured vehicles laden with explosives, destroying clusters of homes in the Sheikh Radwan, Zeitoun, and Tuffah neighbourhoods.
On Sunday, US President Donald Trump suggested a Gaza deal could come soon to secure the release of all the hostages held by Hamas.
Earlier, he issued what he called his "last warning" to the Palestinian militant group.
An Israeli official said Israel was "seriously considering" Trump's proposal but did not elaborate.
The war began with an assault by Hamas-led fighters on southern Israel in 2023.
The attackers killed 1200 people and took more than 250 hostages to Gaza.
Most of the hostages were released in ceasefires in November 2023 and January-March 2025, but the group has held on to others as a bargaining chip in negotiations.
Israel's assault has reduced much of the enclave to rubble and caused a humanitarian catastrophe.
Nearly 63,000 Palestinians have been confirmed killed, according to health officials in the enclave.
Six more Palestinians, including two children, have died of malnutrition and starvation in Gaza in the past 24 hours, the territory's health ministry said on Monday, raising deaths from such causes to at least 393 people, most in the past two months.
Israel, which controls all supplies into Gaza, says the extent of hunger there has been exaggerated and the reported deaths are due to other causes.
Throughout the conflict, efforts to negotiate an end to the war have faltered over Israel's condition that Hamas free all hostages and surrender.
Hamas says it will not lay down its arms until Palestinians have an independent state.]
