The office of Israeli Prime Minister Benjamin Netanyahu on Sunday said Israeli officials would not compromise on the transferring of remains of hostages taken by Hamas, saying it's seeking the return of "every last one of them."

"The Hamas terrorist organization is required to uphold its commitments to the mediators and return them as part of the implementation of the agreement," Netanyahu’s office said in a statement.

Israel "will not compromise" on their return, the office said, adding that it would "spare no effort until we return all of the fallen hostages, every last one of them."

Israeli officials on Sunday morning separately said they had identified one set of remains returned overnight. Another set of remains were in the process of being identified.

Prior to those two bodies being transferred, Hamas had handed over 10 sets of remains out of the 28 that had been in Hamas’ possession when the ceasefire came into effect, according to Israel. Another set of remains handed over did not match any of the missing hostages, Israel said.

Hamas in a statement on Saturday said the recovery and handover of remains may be delayed if Israel does not reopen the Rafah crossing at the border between Gaza and Egypt.

"Specialized" equipment to locate remains, along with personnel who could examine and identify them, were being blocked from entry into Gaza, Hamas said.

The body of Ronen Engel was among the two sets of remains handed over by Hamas and escorted out of Gaza by Israeli military and security officials overnight, the Israel Defense Forces said early on Sunday.

Engel, who was 54 when Hamas attacked Israel in October 2023, had been a volunteer medic with Magen David Adom, the Israeli emergency services, the IDF said. He had been living in Nir Oz, a kibbutz in southern Israel.

"Ronen Tommy Engel was killed by Hamas terrorists on October 7th, 2023, when he went out to defend his family from terrorists, and his body was taken into Gaza," the IDF said on social media.

Engel’s wife, Karina, and two daughters, Mika and Yuval, were also taken hostage by Hamas, according to the IDF. They were released in November 2023 as part of a hostage-release agreement, Lt. Col. Nadav Shoshani, an IDF spokesperson, said on social media on Sunday.

Engel was pronounced dead on Jan. 12, 2023, the military said.

"The Government of Israel shares in the deep sorrow of the Engel family and all the families of the fallen hostages," Prime Minister Benjamin Netanyahu's office said in a statement on Sunday.

Two coffins had been transferred overnight from Hamas to the International Committee of the Red Cross in Gaza, according to Israel. The IDF and Shin Bet, the internal security service, then escorted the remains across the border into Israel, officials said.

The second set of remains returned overnight were still being identified by Israel's National Institute for Forensic Medicine, Avichay Adraee, another IDF spokesperson, said on Sunday.

The State Department said in a statement published Saturday that the United States has informed the guarantor nations of the Gaza peace agreement of "credible reports indicating a ceasefire violation" by Hamas against Gazans.

The agency warns that should Hamas proceed with the attack, measures will be taken.

"The United States and the other guarantors remain resolute in our commitment to ensuring the safety of civilians, maintaining calm on the ground, and advancing peace and prosperity for the people of Gaza and the region as a whole," the State Department said.

-ABC News' Mariam Khan

Hamas reacted to Israeli government closing the Rafah crossing, calling it a "blatant violation of the terms of the ceasefire agreement."

"The continued closure of the Rafah Crossing — preventing the exit of the wounded and sick, restricting the movement of citizens in both directions, blocking the entry of the specialized equipment needed for search operations for those missing under the rubble, and barring the entry of teams and tools required to examine and identify bodies — will delay the recovery and handover of the bodies," Hamas said in a statement.

Hamas called on mediators to help reopen the crossing.

-ABC News' Samy Zyara