Hamas said it was studying on Saturday the latest Israeli counterproposal regarding a potential ceasefire in Gaza, a day after a delegation from mediator Egypt reportedly arrived in Israel in a bid to jump-start stalled negotiations.

The signs of fresh truce talks came alongside ongoing Israeli preparations for a military push into Gaza's southern city of Rafah and as spillover from the war led to continued attacks across the region.

"Today, the Hamas movement received the official Zionist occupation response to the movement's position, which was delivered to the Egyptian and Qatari mediators on 13 April," Khalil al-Hayya, deputy head of Hamas's political arm in Gaza, said in a brief statement early Saturday.

"The movement will study this proposal, and upon completion of its study, it will submit its response."

Hamas had previously insisted on a permanent ceasefire, something rejected by Israel.

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

Several Israeli media outlets, citing unnamed officials, said Israel's war cabinet had discussed a new plan for a truce and hostage release ahead of the Egyptian delegation's visit.