By James Mackenzie, Maayan Lubell and Alexander Cornwell

JERUSALEM (Reuters) - The Israeli military said on Friday that one of the bodies released by Hamas did not belong to any of the hostages held in Gaza, accusing Hamas of violating an already shaking ceasefire.

Two of the bodies were identified as infant Kfir Bibas and his four-year-old brother Ariel, while a third body that was supposed to be their mother, Shiri, was found not to match with any hostage and remained unidentified, the military said.

"This is a violation of utmost severity by the Hamas terrorist organization, which is obliged under the agreement to return four deceased hostages," the military said, in a statement, demanding the return of Shiri and all hostages.

The family of hostage Oded Lifshitz, said in a statement that his body had been formally identified.

There was no immediate reaction from Hamas.

Israeli Prime Minister Benjamin Netanyahu earlier vowed revenge on Hamas after the group released the remains of what it said were four hostages, including that of Kfir and Ariel, the youngest of those abducted during the October 7, 2023, attack.

Palestinian militants handed over four black coffins in a carefully orchestrated public display as a crowd of Palestinians and dozens of armed Hamas militants watched, creating a spectacle which was condemned by U.N. Secretary-General Antonio Guterres.

The purported remains of the boys, their mother and Lifshitz, were handed over under the Gaza ceasefire agreement reached last month with the backing of the United States and the mediation of Qatar and Egypt.

Israelis lined the road in the rain near the Gaza border to pay their respects as the convoy carrying the coffins drove by.

"We stand here together, with a broken heart. The sky is also crying with us and we pray to see better days," said one woman, who gave her name only as Efrat.

In Tel Aviv, people gathered, some weeping, in a public square opposite Israel's defence headquarters that has come to be known as Hostages Square.

"Agony. Pain. There are no words. Our hearts — the hearts of an entire nation — lie in tatters," said President Isaac Herzog.

In a recorded address released after the remains of the hostages were handed over, Netanyahu vowed to eliminate Hamas, saying "the four coffins" obliged Israel to ensure "more than ever" that there was no repeat of the October 7 attack.

"Our loved ones' blood is shouting at us from the soil and is obliging us to settle the score with the despicable murderers, and we will," he said.

Over the course of the 16-month-old conflict, Israeli officials have repeatedly asserted that Hamas would be destroyed and the roughly 250 hostages abducted during the October 2023 Hamas-led attack on Israel would be returned home.

During Thursday's handover, one militant stood beside a poster showing coffins wrapped in Israeli flags. It read "The Return of the War = The Return of your Prisoners in Coffins".

U.N. chief Guterres condemned "the parading of bodies and displaying of the coffins of the deceased hostages in the manner seen this morning, which is abhorrent and appalling," his spokesperson, Stephane Dujarric, said.

He said international law required remains to be handed over in a way that ensures "respect for the dignity of the deceased and their families."

'SYMBOL'

Kfir Bibas was nine months old when the Bibas family, including their father Yarden, was abducted at Kibbutz Nir Oz, one of a string of communities near Gaza that were overrun by Hamas-led attackers from Gaza.

Hamas said in November 2023 that the boys and their mother had been killed in an Israeli airstrike, but their deaths were not confirmed by Israeli authorities.

"Shiri and the kids became a symbol," said Yiftach Cohen, of the Nir Oz kibbutz, which lost around a quarter of its residents, either killed or kidnapped, during the assault.

Yarden Bibas was returned alive in an exchange for prisoners this month.

Lifshitz was 83 when he was abducted from Nir Oz, the kibbutz he helped found. His wife, Yocheved, 85 at the time, was seized with him and released two weeks later, along with another woman.

He was a former journalist and in an op-ed in left-leaning Haaretz in January 2019, he listed what he said were Netanyahu's policy failures.

LIVING HOSTAGES

The handover marked the first return of dead bodies during the current agreement.

The military said that the Bibas children had been murdered in captivity in November 2023 by "terrorists". The prime minister's office earlier said that Lifshitz was murdered in captivity by Islamic Jihad, another militant group in Gaza.

Chen Kugel, the head of the Israel National Center of Forensic Medicine, later said in a televised statement that Lifshitz had been murdered more than a year ago.

The Hamas-led attack into Israel killed some 1,200 people, according to Israeli tallies, with 251 kidnapped. Israel's subsequent military campaign has killed some 48,000 people, Palestinian health authorities say, and left densely populated Gaza in ruins.

Thursday's handover of bodies will be followed by the return of six living hostages on Saturday, in exchange for hundreds more Palestinians, expected to be women and minors detained by Israeli forces in Gaza during the war.

Negotiations for a second phase, expected to cover the return of around 60 remaining hostages, less than half of whom are believed to be alive, and a full withdrawal of Israeli troops from the Gaza Strip to allow an end to the war, are expected to begin in the coming days.

(Reporting by James Mackenzie and Maayan Lubell in Jerusalem; Additional reporting by Alexander Cornwell in Jerusalem, Jana Choukeir and Nayera Abdullah in Dubai and Ilan Rozenberg near Reim and Emma Farge in Geneva; Writing by James Mackenize and Michael Georgy; Editing by Cynthia Osterman and Stephen Coates)