A video still shows a man who identified himself as Keith Siegel speaking to a camera. AFP

Hamas said on Saturday it was studying Israel's latest counterproposal for a Gaza ceasefire, a day after media reports said a delegation from mediator Egypt was in Israel trying to jump-start stalled negotiations.

The armed wing of Hamas also released video footage of two men held hostage in Gaza, identified by Israeli campaign group the Hostages and Missing Families Forum as Keith Siegel and Omri Miran.

The signs of fresh truce talks come after the United Nations warned that "famine thresholds in Gaza will be breached within the next six weeks" unless massive food assistance arrives.

Aid groups say Gaza's already catastrophic humanitarian conditions would be worsened by Israel's vow to attack Hamas fighters still in Rafah city in southernmost Gaza.

Rafah, on the border with Egypt, is crowded with hundreds of thousands of Palestinians displaced by nearly seven months of war between Israel and the Islamist movement.

"We live in constant terror and fear of repeated displacement and invasion," Nidaa Safi, 30, who fled Israeli strikes in the north and came to Rafah with her husband and children, told the media.

An image grab from a video shows a man who identified himself as Omri Miran speaking to a camera. AFP

The area comes under regular bombardment. Hospital officials said strikes in Rafah and elsewhere killed more than a dozen people overnight.

Among the dead were an entire family, their relative Mohammed Yussef said.

"Nobody left: the father, the mother, a girl and two boys" were killed when their house was targeted, he said.

Daily deaths

Khalil Al Hayya, deputy head of Hamas's political arm in Gaza, said it had "received the official Zionist occupation response to the movement's position, which was delivered to the Egyptian and Qatari mediators on April 13".

In a statement, Hayya said Hamas "will study this proposal" before responding.

The movement has previously insisted on a permanent ceasefire, which Israel rejects.

Egypt, Qatar and the United States have been unsuccessfully trying to seal a new Gaza truce deal ever since a one-week halt to the fighting in November saw 80 Israeli hostages exchanged for 240 Palestinians held in Israeli prisons.

Al-Qahera News, which is linked to Egyptian intelligence services, reported "noticeable progress in bringing the views of the Egyptian and Israeli delegations closer".

In early April, Hamas had said it was studying a proposal, after talks in Cairo, and Al-Qahera reported progress. Days later Israel and Hamas accused each other of undermining negotiations.

Dozens are dying in Gaza every day, according to the health ministry in the Hamas-run territory.

The war began with Hamas's unprecedented October 7 attack which resulted in the deaths of about 1,170 people in Israel, mostly civilians, according to an AFP tally of Israeli official figures.

Agence France-Presse