Hamas has agreed to the latest proposal from regional mediators for a Gaza ceasefire and hostage release deal with Israel, a source in the Palestinian armed group has told the BBC.

The proposal from Egypt and Qatar is said to be based on a framework put forward by US envoy Steve Witkoff in June.

It would see Hamas free around half of the 50 remaining Israeli hostages - 20 of whom are believed to be alive - in two batches during an initial 60-day truce. There would also be negotiations on a permanent ceasefire.

It is unclear what Israel's response will be, as Prime Minister Benjamin Netanyahu's office said last week that it would only accept a deal if "all the hostages are released in one go".

In a video released after the reports of Hamas's approval emerged, Netanyahu did not comment directly but said that "from them you can get one impression - Hamas is under immense pressure."

The Israeli military's chief of staff, Lt Gen Eyal Zamir, meanwhile said it was at a turning point in the 22-month war, with the "focus on enhancing the strikes against Hamas in Gaza City".

It came as witnesses on the ground in Gaza City reported that Israeli tanks backed by air and artillery strikes had made a surprise advance into the southern Sabra neighbourhood, and surrounded schools and a UN-run clinic sheltering hundreds of displaced people.

Later this week, the Israeli cabinet is expected to approve the military's plan to occupy Gaza City, where intensifying Israeli strikes have already prompted thousands of people to flee.

Netanyahu announced Israel's intention to widen its offensive and conquer all of Gaza - including the areas where most of its 2.1 million Palestinian residents have sought refuge - after indirect talks with Hamas on a ceasefire deal broke down last month.

A Hamas delegation led by the group's chief negotiator, Khalil al-Hayya, has been in Cairo since last week meeting mediators who see a window of opportunity for a new agreement.

On Monday morning, a senior Hamas official told the BBC that the delegation was reviewing a new ceasefire proposal that it had received the previous day.

Qatar's Prime Minister, Sheikh Mohammed bin Abdul Rahman Al Thani, also visited the Egyptian capital to "apply maximum pressure on the two sides to reach a deal as soon as possible", Egyptian Foreign Minister Badr Abdelatty said.

Speaking during his own trip to the Rafah border crossing with Gaza, Abdelatty stressed the urgency of reaching a ceasefire to alleviate the deep humanitarian crisis in the Palestinian territory. He said the current situation on the ground there was "beyond imagination".

On Monday evening, a Hamas source told the BBC that the group had submitted a written response to mediators saying it agreed to the ceasefire proposal without any amendments or conditions.

According to a Palestinian official familiar with the talks, the proposal "mirrors" the one presented by Steve Witkoff two months ago, which Hamas rejected.

Witkoff proposed a 60-day truce that would see the release of 10 living hostages by Hamas and the bodies of 18 other hostages in exchange for Palestinian prisoners held in Israeli jails. He also said that serious negotiations to end the war would take place during the truce.

On Sunday night, hundreds of thousands of Israelis gathered in Tel Aviv to demand that their government agree a deal with Hamas to end the war now and bring all the hostages home.

Hostages' families fear that another offensive in Gaza City could endanger those held there.

"I'm scared that my son would be hurt," said Dani Miran, whose 48-year-old son Omri has been held captive for 682 days.

Netanyahu accused the demonstrators of hardening Hamas's negotiating position.

Palestinians also called for an immediate end to the war at a protest in Gaza City on Monday.

"Hamas and its demands, and the demands being negotiated, do not represent me. I want to live in peace. I want peace of mind. Our only demand is peace and safety for our children," one woman told a local freelance journalist working for the BBC.

US President Donald Trump meanwhile wrote on social media: "We will only see the return of the remaining hostages when Hamas is confronted and destroyed!!! The sooner this takes place, the better the chances of success will be."

Israel's prime minister has said the war will only end once all the hostages are released and Hamas disarms. He also wants Gaza to be demilitarised, kept under Israeli security control, and run by an administration not linked to Hamas or the Palestinian Authority.

Hamas has called for a comprehensive deal that would see the hostages it is holding exchanged for Palestinian prisoners in Israeli jails, as well as an end to the war and the full withdrawal of Israeli forces from Gaza. It says it will not disarm unless an independent Palestinian state is created.

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

At least 62,004 people have been killed in Gaza since then, according to the territory's Hamas-run health ministry.

Most of Gaza's population has also been displaced multiple times; more than 90% of homes are estimated to be damaged or destroyed; the healthcare, water, sanitation and hygiene systems have collapsed; and UN-backed global food security experts have warned that the "worst-case scenario of famine is currently playing out" due to food shortages.

Gaza's health ministry reported on Monday that another five people, including two children, had died as a result of malnutrition over the previous 24 hours, raising the total number of such deaths since the start of the war to 263.