Palestinian militant group Hamas on Thursday handed over Israeli woman hostage Agam Berger, a soldier, as a third hostage-prisoner exchange got under way, an AFP journalist reported.

Three Israelis and five Thai captives are slated for release Thursday under a ceasefire deal aimed at ending the Gaza war.

Berger, dressed in military fatigues, was paraded by Hamas militants on a stage in Jabalia in the northern Gaza Strip before being handed over to International Committee of the Red Cross officials.

Israel's military said she was back in Israel and would undergo "an initial medical assessment."

Earlier, Prime Minister Benjamin Netanyahu's office identified the three Israelis to be freed Thursday as Arbel Yehud, Berger, and Gadi Moses, adding that five Thais held in Gaza would also be freed.

Ahead of the release, which sources in Hamas and allied militant group Islamic Jihad said would take place at Jabalia refugee camp and Khan Yunis, Islamic Jihad aired video footage of Moses and Yehud hugging each other and smiling.

On Wednesday, the Moses family said it had "received with great excitement the wonderful news of our beloved Gadi's return."

A fourth exchange is scheduled for the weekend, but Hamas accused Israel on Wednesday of jeopardising the deal by holding up aid deliveries, an allegation Israel dismissed as "fake news."

The ceasefire that began on 19 January hinges on the release of Israeli hostages taken during Hamas' 7October 2023 attack, in exchange for 1,900 people — mostly Palestinians — in Israeli custody.

Before Berger was handed over Thursday, Hamas had released seven hostages, with 290 prisoners freed in exchange. 

Israel is to release 110 prisoners, including 30 minors, in exchange for the three Israelis, the Palestinian Prisoners' Club advocacy group said.

The next swap on Saturday will see three Israeli men released, according to Netanyahu's office.

Aid trucks row

The truce deal has allowed truckloads of aid into the devastated Gaza Strip, where the war has created a long-running humanitarian crisis.

However, senior Hamas officials accused Israel of slowing aid deliveries, with one citing key items such as fuel, tents, heavy machinery and other equipment.

"According to the agreement, these materials were supposed to enter during the first week of the ceasefire," one official said.

"We warn that continued delays and failure to address these points will affect the natural progression of the agreement, including the prisoner exchange."

COGAT, the Israeli defence ministry body that oversees civilian affairs in the Palestinian territories, called this "totally fake news."

Between Sunday and 1100 GMT on Wednesday, "3,000 trucks entered Gaza," a spokesman said. 

"The agreement says it should be 4,200 in seven days," he added.

As the text of the agreement — mediated by Qatar, Egypt and the United States — has not been made public, AFP was not able to verify its terms on aid.

Displacement 'injustice'

The ceasefire deal is currently in its first, 42-day phase, which should see 33 hostages freed. The Thai hostages are not included in that number.

Next, the parties are due to start discussing a long-term end to the war. 

The third and final phase of the deal should see the reconstruction of Gaza and the return of any remaining dead hostages.

US President Donald Trump has repeatedly claimed credit for sealing the agreement despite it taking effect before his inauguration, and his Middle East envoy Steve Witkoff, who took part in the talks, met Netanyahu in Israel on Wednesday.

Trump has invited Netanyahu to the White House on February 4, according to the premier's office.

After the truce took effect, Trump touted a plan to "clean out" Gaza, calling for Palestinians to relocate to neighbouring countries such as Egypt or Jordan.

However, Egyptian President Abdel Fattah al-Sisi said Wednesday the forced displacement of Palestinians was an "injustice that we cannot take part in."

Jordan's King Abdullah II stressed "the need to keep the Palestinians on their land and to guarantee their legitimate rights, in accordance with the Israeli and Palestinian two-state solution".

More than 376,000 displaced Palestinians have gone back to northern Gaza since Israel reopened access earlier this week, according to the UN humanitarian office OCHA, with many returning to little more than rubble.

"My house is destroyed," 33-year-old Mohammed Al-Faleh told AFP. "This morning, we built a small room with two walls made from the remains of our home. There is no cement, so I used mud."

"The biggest problem is that there is no water — all the water wells are destroyed," he added.

"Food aid is reaching Gaza... but there is no gas or electricity. We bake bread on a fire fuelled by wood and nylon."