One of the four bodies handed over by Hamas on Tuesday night is not a missing hostage from Gaza, the Israeli military has said, as the country’s far-right security minister called for a total halt on humanitarian aid into the strip.

The bodies were released late on Tuesday evening after the Israeli government threatened to keep the road between Gaza and Egypt closed and halve the expected flow of aid into the strip.

The moves came amid the despair and anger of grieving families that only four of the missing 28 deceased hostages had been released on Monday when the 20 Israelis still alive in Gaza came home.

The ceasefire agreement requires Hamas to make every effort to return the missing bodies in exchange for those of 360 Palestinians killed in the war in Gaza.

After the release of the remains of what Hamas said were four more hostages, the Israeli government appeared on Wednesday morning to have relented on their threats, but only three of those handed over have since been identified as missing Israelis.

The Israeli military said on Wednesday that one of the bodies handed over by Hamas “does not match any of the hostages”, after examinations at the National Institute of Forensic Medicine in Tel Aviv. “Hamas is required to make all necessary efforts to return the deceased hostages,” it said.

Itamar Ben-Gvir, Israel’s security minister, said Hamas was ‘playing games’ and called on Benjamin Netanyahu to issue ‘a clear ultimatum’. Photograph: Chip Somodevilla/Reuters

Israel has repeatedly blocked aid from entering Gaza during the conflict, prompting accusations it has used starvation as a weapon of war. Humanitarian officials have repeatedly warned that assistance is desperately needed. Famine was declared in parts of Gaza in August.

Speaking on Tuesday, Itamar Ben-Gvir, who is a security minister despite having been convicted in 2007 of racist incitement and supporting groups on terrorism blacklists, said Hamas was “playing games”.

He said: “Enough with the disgrace. Moments after opening the crossings to hundreds of trucks, Hamas very quickly returned to its known methods – to lie, to cheat, and to abuse families and the bodies. This Nazi terror understands only force, and the only way to deal with it is to erase it from the face of the earth.”

Ben Gvir called on Israel’s prime minister, Benjamin Netanyahu, to issue “a clear ultimatum to Hamas: if you do not immediately return all the bodies of our fallen and you continue with these delays, we will immediately halt all aid supplies entering the [Gaza] Strip”.

The chief of staff of the Israel Defense Forces, Lt Gen Eyal Zamir, said the military would “not rest until we return all [of the hostages]. This is our moral, national and Jewish duty.”

“In coordination with the political echelon, we will insist and stand firm on upholding all the agreements,” he said at a handover ceremony for the chief of the Northern Corps.

The bodies of (from left) Ouriel Baruch, Eitan Levy and Tamir Nimrodi have been identified as three of the four released on Tuesday. Photograph: Supplied

Three of the bodies have been identified as the hostages Staff Sgt Tamir Nimrodi, 18, Ouriel Baruch, 35, and Eitan Levy, 53.

The Hostages and Missing Families Forum said in a statement that Nimrodi had been kidnapped alive on 7 October but “killed by IDF bombings in captivity”.

The body of Baruch, a father of two from Jerusalem, was taken from the Nova music festival, where he was shot dead near his car during the Hamas attack.

Levy, a taxi driver, was killed after dropping off a friend at the Be’eri kibbutz on the morning of the attack and his remains were taken into Gaza the same day.

Under the ceasefire deal, Israel has freed some doctors, nurses and paramedics seized during raids on hospitals in Gaza, but other high-profile medical figures remain missing.

According to the NGO Healthcare Workers Watch (HWW), more than 100 remain in Israeli prisons, including Dr Hussam Abu Safiya, a hospital director, who became the face of the struggle to keep treating patients under Israeli siege and bombardment.

Abu Safiya, the director of the Kamal Adwan hospital in northern Gaza, has been imprisoned without charge by Israel for nearly 10 months.

HWW, which documents detentions from Gaza, said 55 medical workers – including 31 doctors and nurses – were on lists of freed detainees.

The group said at least 115 medical workers remained in custody, as well as the remains of four who died while in Israeli prisons, where rights groups and witnesses have reported frequent abuse.