Hamas says it has delivered a “positive response” to mediators on the latest proposal for a new Gaza ceasefire and hostage release deal put forward by the US.

The Palestinian armed group added in a statement that it was “seriously ready to enter immediately into a round of negotiations”.

A senior Palestinian official familiar with the talks told the BBC that Hamas accepted the general framework but had requested several key amendments, including a US guarantee that hostilities would not resume if talks on a permanent end to the 20-month war failed.

There was no immediate response from Israel and the US. But they have previously been reluctant to accept similar demands.

US President Donald Trump said on Tuesday that Israel had accepted the “necessary conditions” for a 60-day ceasefire, during which the parties would work to end the war.

He also urged Hamas to accept what he described as “the final proposal”, warning the group that “it will not get better – it will only get worse”.

The plan is believed to include the staggered release of 10 living Israeli hostages by Hamas and the bodies of 18 other hostages in exchange for Palestinian prisoners held in Israeli jails. Fifty hostages are still being held in Gaza, at least 20 of whom are believed to be alive.

The proposal also reportedly says that sufficient quantities of humanitarian aid would enter Gaza immediately with the involvement of the UN and the International Committee of the Red Cross.

The senior Palestinian official said Hamas was demanding that the aid be distributed exclusively by the UN and its partners, and that the controversial distribution system run by the Israel- and US-backed Gaza Humanitarian Foundation (GHF) end immediately.

Another key amendment demanded by Hamas was about Israeli troop withdrawals, according to the Palestinian official.

The US proposal is believed to include phased pull-outs from parts of northern and southern Gaza. But the official said Hamas was insisting that troops returned to the positions they held before the last ceasefire collapsed in March, when Israel resumed its offensive against the group.

The Palestinian official said Hamas also wanted a US guarantee that Israeli air and ground operations would not resume if negotiations on a permanent ceasefire failed.

The proposal is believed to say that negotiations on ending the war would begin on day one.

However, Israel’s Prime Minister Benjamin Netanyahu has ruled out ending the war until all of the hostages are released and Hamas’s military and governing capabilities are destroyed.

The Israeli military continued to bomb targets across the Gaza Strip as the US and Israel awaited Hamas’s response to the ceasefire proposal on Friday.

Gaza’s Hamas-run health ministry said in the afternoon that Israeli attacks had killed at least 138 Palestinians over the previous 24 hours.

Overnight, at least 15 Palestinians were killed in strikes on two tents housing displaced people in the southern Khan Younis area, the local Nasser hospital said.

Thirteen-year-old Mayar al-Farr’s brother, Mahmoud, was among those killed.

“The ceasefire will come, and I have lost my brother? There should have been a ceasefire long ago before I lost my brother,” she told Reuters news agency at his funeral.

Adlar Mouamar, whose nephew Ashraf was also killed, said: “Our hearts are broken… We want them to end the bloodshed. We want them to stop this war.”

The Israeli military has not yet commented on the strikes, but did say its forces were “operating to dismantle Hamas military capabilities”.

Later on Friday, the ICRC said a staff member at the Red Cross field hospital in Rafah, in southern Gaza, had been hit by a stray bullet. His condition was stable after the “unacceptable” incident, the ICRC said.

Meanwhile, medical charity Médecins Sans Frontières said a former colleague had been killed the previous day when, it said, Israeli forces fired on people waiting for aid lorries in Khan Younis. At least 16 people were killed in the incident, MSF quoted teams at Nasser hospital as saying. The Israeli military has not yet commented.

“The systemic and deliberate starvation of Palestinians for over 100 days is pushing people in Gaza to breaking point,” said Aitor Zabalgogeazkoa, MSF’s emergency co-ordinator in Gaza. “This carnage must stop now.”

The UN human rights office said on Friday that it had recorded the killing of at least 509 people near the GHF’s aid distribution centres and 104 other people near aid convoys.

Spokeswoman Ravina Shamdasani said the office was working to verify the figures and ascertain who was responsible, but added that it was “clear that the Israeli military has shelled and shot at Palestinians trying to reach the distribution points”.

The GHF said the UN figures were coming “directly” from the Gaza health ministry, which it says is not credible, and that they were being used to “falsely smear” its effort. Its chairman insisted this week there had not been any violent incidents at or in close proximity to its sites.

The Israeli military has said it is examining reports of civilians being harmed while approaching the GHF’s sites, but insisted that reports of “extensive casualties” at them are “lies”.

In the Israeli city of Tel Aviv, only 60km (40 miles) from Gaza, the families of the remaining hostages and their supporters held a rally outside the US embassy branch office, urging Trump to “make the deal” that would see them all released.

On the nearby beachfront, they laid out a giant banner featuring the US flag and the words “liberty for all”.

Among those who addressed the event was Ruby Chen, the father of Israeli-American Itay Chen. The 19-year-old soldier was killed during the Hamas-led attack on southern Israel on 7 October 2023 which triggered the war, and his body was taken back to Gaza as a hostage, according to the Israeli military.

“I urge you Prime Minister Netanyahu to go to the US next week and bring back a deal that brings all the hostages home,” Mr Chen said. “There has to be a final, detailed agreement between Israel and Hamas.”

Keith Siegel, an Israeli American who was released in February during the last ceasefire after 484 days in captivity, also spoke.

“Many of my friends from Kibbutz Kfar Aza remain in captivity,” he said. “Only a comprehensive deal can bring them all home and create a better future for the Middle East.”

The primary concern for most Israelis is the fate of the remaining hostages and what might happen to them if the ceasefire does not happen and Netanyahu orders the Israeli military to step up its air strikes on Gaza.

On Thursday, the prime minister promised to secure the release of all the remaining hostages during a visit to Kibbutz Nir Oz, a community near the Israel-Gaza border where a total of 76 residents were abducted on 7 October 2023.

“I feel a deep commitment, first of all, to ensure the return of all of our hostages, all of them,” he said. “We will bring them all back.”

The Israeli military launched a campaign in Gaza in response to the 7 October 2023 attack, in which about 1,200 people were killed and 251 others were taken hostage.

At least 57,268 people have been killed in Gaza since then, according to the territory’s health ministry.

Additional reporting by David Gritten in Jerusalem