U.S. mediator Jared Kushner and Israeli Prime Minister Benjamin Netanyahu held talks on Monday on the second phase of the Gaza ceasefire.

The two discussed some of the most sensitive aspects of the agreement's phase two, Israeli government spokeswoman Shosh Bedrosian told the media.

"Together, the two discussed phase one, which we are currently still in, to bring our remaining hostages, and the future of phase two of this plan, which includes the disarming of Hamas, demilitarizing Gaza and ensuring Hamas will have no role in the future of Gaza ever again," Bedrosian said.

"Phase two also includes the establishment of the international stabilization force, and the details of which of course together are being discussed."

Hamas has repeatedly insisted that relinquishing its weapons is a red line.

Fragile ceasefire

The truce in Gaza, in effect for exactly a month now, has largely halted the conflict that erupted after Hamas's surprise attack on Israel on October 7, 2023. During the ongoing first stage, a series of prisoner and hostage exchanges took place.

Despite the progress, Israel and Hamas continue to accuse each other of violating the ceasefire, while Israel has intensified its attacks against Hezbollah in Lebanon despite a truce since November.

Gaza's health authorities claimed Israeli forces have killed at least 242 Palestinians in the territory since the ceasefire began on October 10.

Hamas spokesperson Hazem Qasim on Monday accused Israel of deliberately expanding the "Yellow Line" area in northern Gaza, effectively altering the control boundaries between the two sides after the ceasefire. He added that recent Israeli military operations in several areas constitute a "systematic violation" of the ceasefire agreement.

Qasim also said that Hamas has informed mediators that heavy machinery is needed to search for the bodies of Israeli captives under the rubble, but the ongoing restrictions imposed by Israel have hindered the operation.

'Iron fist'

On Monday, the Israeli military said it killed two militants who approached the "Yellow Line."

"Whoever seeks to harm us, we harm them," Netanyahu said in parliament on Monday. "We are determined to enforce with an iron fist the ceasefire agreements where they exist against those who seek our destruction, and you can see what happens every day in Lebanon," he said.

Israel has kept up attacks on Lebanon, where it says it is targeting Hezbollah militants. It agreed a ceasefire with the group last November, but has frequently bombed Lebanon since then. It said on Monday it had killed 15 Hezbollah members since the start of November.

Egypt, Qatar and Türkiye are among the potential participants in the proposed international stabilization force for Gaza, but the United Arab Emirates has indicated it is unlikely to join without a clear operational framework.

"Under such circumstances, the UAE will probably not participate in such a force," Emirati presidential adviser Anwar Gargash told the Abu Dhabi Strategic Debate Forum on Monday.

Türkiye has expressed willingness to join, but Netanyahu has repeatedly said Israel would not allow it.

"The prime minister said... there will be no Turkish boots on the ground," Bedrosian said.

Türkiye has been one of the most outspoken critics of the Gaza conflict, and on Friday it issued arrest warrants, accusing Netanyahu and several senior Israeli officials of genocide.

'Life in Gaza is hard'

Since the truce began, Hamas has returned all 20 living hostages and the remains of 24 captives, including 21 Israelis. Four bodies of hostages killed in the October 2023 attack remain in Gaza.

In exchange, Israel has freed nearly 2,000 prisoners and returned 315 bodies of Palestinian captives.

Despite the progress in hostage returns, Gazans remain anxious about their future.

"We still do not feel safe. Shooting continues ... we try to protect our children from psychological trauma and to help them forget the war and its effects," said Salma Abu Shawish, 40, a resident of Al-Bureij refugee camp in central Gaza.

"Life in Gaza is hard. We still lack food, and many families remain homeless. We only wish this nightmare would stop and never return."

(With input from agencies)