Diplomatic efforts intensified on Sunday to reach a long sought-after truce and hostage-release deal in Gaza, as Hamas said it would travel to mediator Egypt to deliver its response to Israel's latest proposal.

The Israeli government has come under intense pressure to reach a ceasefire from its global allies, as well as from protesters within Israel demanding the release of hostages seized by Hamas during their October 7 attack that triggered the war.

A Hamas delegation will arrive in Egypt on Monday to deliver the group's response to Israel's new hostage and truce counterproposal, a senior official of the militant group said.

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

Hamas has previously insisted on a permanent ceasefire – a condition that Israel has rejected.

However the Axios news website, 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.

A Hamas source close to the negotiations said that the group "is open to discussing the new proposal positively."

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 siege" in Gaza.

The new hopes of a potential truce came as world leaders and humanitarian groups warned that a looming Israeli invasion of the southernmost city of Rafah would lead to massive civilian causalities.

Palestinian president Mahmoud Abbas appealed to the US to stop Israel from invading Rafah, which he said would be "the biggest disaster in the history of the Palestinian people." (AFP)