The beach at Zikim where Mr Mengistu is believed to have crossed into the Gaza Strip. Photo: AP

Lifting a long-standing gag order, Israel admitted on Thursday that two of its citizens have been missing in Gaza for months as signs emerged that it was attempting to negotiate with Hamas for their release.

Avera Mengistu, a 28-year-old Israeli-Ethiopian, went missing 10 months ago when he is believed to have left his home in Ashkelon in Israel's south and climbed over a border fence near Zikim beach to enter Gaza.

Local media reported that he is believed to have suffered psychological problems in the past.

Avera Mengistu in a photo provided by his family. Photo: Reuters

The second man who has not been named is believed to be a Bedouin who crossed into Gaza several months ago.

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Little is known about the whereabouts of the two men, although Israeli authorities say they believe Hamas is holding Mr Mengistu and is using his capture as a bargaining tool in negotiations over the return of the bodies of two Israeli soldiers killed during last year's war in Gaza.

Staff Sergeant Oron Shaul and First Lieutenant Hadar Goldin were killed in separate incidents during the 50-day war in Gaza last year, in which 2205 Palestinians were killed – at least 66 per cent of them civilians – as well as 66 Israeli soldiers, six Israeli civilians and a Thai national.

Avera Mengistu's brother Ilan speaks to the media outside the family home in the southern city of Ashkelon. Photo: Reuters

Hamas denies holding Mr Mengistu, although the head of its political bureau, Khaled Meshal, said Israel had approached Hamas via European mediators to request the release of two prisoners and the bodies of two soldiers being held in Gaza.

Speaking to reporters in Doha, Mr Meshal indicated Hamas would not agree to negotiations until Israel released more than 70 prisoners who had been freed under the deal to release captured IDF soldier Gilad Shalit and then rearrested by the Israeli military.

In 2011, Germany helped to broker the controversial prisoner swap that resulted in the release of Mr Shalit, who had been held in Gaza for more than five years, in exchange for 1027 Palestinian prisoners.

Yaakov Peri, a member of the Knesset for the Yesh Atid party and a former head of the Israeli security service Shin Bet, said he was unable to elaborate on whether there were any ongoing negotiations with Hamas over the release of the two Israeli citizens or the soldiers' bodies.

"We are making every possible effort to bring Mr Mengistu back and of course the bodies of the soldiers," Mr Peri told journalists via a phone hook-up.

"He is not a soldier, he passed [into Gaza] of his own free will, but we see it as our obligation and Hamas' obligation to bring him back safely … I hope we are able to make a deal and to bring back the bodies of our soldiers and Mr Mengistu and if there are others as well."

Mr Mengistu's family have been critical of the Israeli government's handling of his disappearance, saying if he was white they would have done more to resolve the situation.

A blanket embargo was imposed last year on publishing any details about his case, and was only lifted on Thursday at the request of the Israeli newspaper Haaretz.

His brother Yalo told Haaretz: "We are fed up. We want to go public with his story … I am one million per cent certain that if he were white, we would not have come to a situation like this."