Hamas last claimed firing rockets at Tel Aviv in May.
One strike killed six people in Deir al-Balah, including a mother and her twin four-day-old babies, while seven other Palestinians were killed in a strike on a house in the nearby al-Bureij camp.
Four people were killed in two separate strikes on the al-Maghazi camp in the central Gaza Strip and Rafah in the south, and two were killed in a strike on a house in the Sheikh Radwan neighbourhood of Gaza City in the north, medics said.
The Israeli military and Islamic Jihad and Hamas said they were fighting in several areas of Gaza.
The Israeli military said it had killed Palestinian gunmen and dismantled military structures in Khan Younis, located weapons and explosives in Rafah, and struck rocket launchers and sniper posts in central Gaza.
The US said on Monday that it expected Gaza ceasefire talks slated for Thursday to go ahead as planned, and that an agreement was still possible.
Axios reported that US Secretary of State Antony Blinken planned to set off on Tuesday for discussions in Qatar, Egypt and Israel.
The Israeli Government said it would send a delegation to Thursday’s talks to finalise the details of the agreement proposal.
But Hamas is demanding a workable plan to implement the proposal, presented by US President Joe Biden in May – rather than more talks.
A Hamas official told Reuters that a CNN report saying the group planned to attend on Thursday was wrong.
“Our statement the other day was clear: what is needed is the implementation, not more negotiation,” said the official, who declined to be named owing to the sensitivity of the issue.
The war was triggered when Hamas-led fighters stormed into Israel on October 7, killing 1200 people and taking about 250 hostage back to Gaza, according to Israeli tallies.
Almost 40,000 Palestinians have since been killed in the Israeli offensive in Gaza, with much of the enclave laid to waste and most of the population displaced.
A ceasefire deal would aim to end fighting in Gaza and ensure the release of Israeli hostages held in the enclave in return for Palestinians jailed in Israel.
In Deir al-Balah, one of the most overcrowded places in Gaza with hundreds of thousands of displaced, many were desperate for a truce.
“Enough, we are no longer able to tolerate the war, the starvation and the frequent displacement,” said Ghada, a mother of six who two days ago had to leave her tent in Khan Younis under new Israeli evacuation orders.
“I hope this time they will reach a ceasefire. If they don’t, I don’t know how much longer we can survive,” she told Reuters via a chat app.
