On Sunday night, Israeli Prime Minister Benjamin Netanyahu's office announced that Israel had "agreed to a limited reopening of the Rafah crossing for pedestrian passage only, subject to a full Israeli inspection mechanism".

The Israeli military was "currently conducting a focused operation to exhaust all of the intelligence that has been gathered in the effort to locate and return" the remains of Ran Gvili, a statement said.

"Upon completion of this operation, and in accordance with what has been agreed upon with the US, Israel will open the Rafah crossing," it added.

Israel's Haaretz newspaper cited a source as saying there would be a "full Israeli monitoring mechanism" at the crossing, which would include oversight of entry and exit lists.

Israel also planned to establish an additional screening point for all people entering Gaza located in an area around the Yellow Line, which demarcates the territory still controlled by Israeli forces under the ceasefire deal, the source added.

Earlier on Sunday, the Israeli military said troops had "begun a targeted operation in the area of the Yellow Line in the northern Gaza Strip" to retrieve Gvili's body.

Israeli military officials told local media that the operation was acting on intelligence collected over a long period of time, which indicated that Gvili's remains might have been buried in the Shejaiya and Daraj Tuffah areas of Gaza City, east of the Yellow Line.

Specialised units were on the ground, including rabbis, search teams and dental experts equipped with mobile X-ray machines, they added.

Hamas's military wing, the Izzedine al-Qassam Brigades, said on Sunday that it had "provided mediators with all the details and information in our possession regarding the location" of Gvili's body.

Israeli forces were "searching one of the sites," it added.

Gvili's family meanwhile reiterated their strong opposition to the reopening of the Rafah crossing before his body had been returned to Israel for burial. "First and foremost, Ran must be brought home," they said.

The 24-year-old was killed in Kibbutz Alumim during the Hamas-led attack on southern Israel on 7 October 2023 and his body was taken back to Gaza as a hostage.

At the start of December, the Israeli government said the Rafah crossing would open "in the coming days" to allow Palestinians to leave Gaza.

However, a dispute emerged with Egypt, which said the crossing would only be opened if movement was allowed in both directions, enabling the return of tens of thousands of Palestinians who fled Gaza during the war.

On Saturday, US special envoy Steve Witkoff and Trump's son-in-law Jared Kushner led a delegation which met Israel's prime minister for discussions focused on the implementation of phase two of the Gaza peace plan. Witkoff said the meeting was "constructive and positive".

Under phase one, Hamas and Israel agreed to the ceasefire, an exchange of all living and dead Israeli hostages in Gaza for Palestinians detained in Israeli jails, a partial Israeli withdrawal, and a surge in deliveries of humanitarian aid.

Phase two should see a new technocratic Palestinian government in Gaza take over running public services, as well as the reconstruction and full demilitarisation of the territory, including disarmament of Hamas and other groups.

The war was triggered by the 7 October 2023 attack, when about 1,200 people were killed and 251 others taken to Gaza as hostages.

Israel responded by launching a military campaign in Gaza, during which more than 71,650 people have been killed, according to the territory's Hamas-run health ministry.