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A senior Hamas official told AFP on Sunday that the group would deliver its response to Israel's latest counter-proposal for a Gaza ceasefire on Monday in Egypt.

"A Hamas delegation headed by Khalil al-Hayya will arrive in Egypt tomorrow... and deliver the movement's response" to the Israeli proposal during a meeting with Egyptian intelligence officials, said the official who declined to be named.

Mediator Egypt had sent its own delegation to Israel this week to jump-start stalled negotiations even as Israel's offensive in the Gaza Strip rages.

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

Diplomatic efforts have been stepped up in recent days to reach a truce and hostage-release deal in Gaza.

US news website Axios, citing two Israeli officials, reported that Israel's latest proposal includes a willingness to discuss the "restoration of sustainable calm" in Gaza after hostages are released.

It is the first time in the nearly seven-month war that Israeli leaders have suggested they are open to discussing an end to the war, Axios said.

"Hamas is open to discussing the new proposal positively," another Hamas source close to the negotiations told AFP.

The source added that the group is "keen to reach an agreement that guarantees a permanent ceasefire, the free return of displaced people, an acceptable deal for (prisoner) exchange and ensuring an end to the [Gaza] siege".