CAIRO, Egypt -- The US and Hamas held their first direct talks since the Gaza ceasefire as part of efforts to advance the fragile US-brokered agreement, two Hamas sources said.

A delegation led by senior US advisor Aryeh Lightstone met chief Hamas negotiator Khalil al-Hayya in Cairo on Tuesday night, according to the sources. Lightstone was joined by Nickolay Mladenov, the US-backed Board of Peace’s High Representative for Gaza, officials said. Contacted for comment by CNN, a State Department spokesperson said, “We don’t comment on ongoing negotiations.”

Al-Hayya, who survived an Israeli assassination attempt in the Qatari capital Doha last September, pressed Lightstone about the need for Israel to fully implement its commitments to the first phase of the agreement — including an end to strikes and the entry of more humanitarian aid — in order to move to the next phase, the sources said.

The truce, brokered in October, brought an end to two years of war in Gaza, even as it failed to answer substantive questions about the future of the devastated territory, including the role of Hamas in any future security or governing role. Hamas has reasserted its control over the portion of Gaza not occupied by Israel and the Israeli military has continued to carry out frequent strikes in the territory.

Tuesday’s meeting came days after Lightstone met with Israeli Prime Minister Benjamin Netanyahu to secure Israel’s commitment to fully implement its requirements under the first phase of the ceasefire, said a US source and a diplomat familiar with the meeting. One source said Israel agreed to implement those requirements if Hamas committed to disarmament.

Meetings between Hamas, representatives of the Board of Peace and international mediators have aimed to reach an agreement over the next phase of the ceasefire deal: the disarmament of Hamas, the deployment of an international force to Gaza, and the withdrawal of Israeli forces from the devastated territory.

But multiple sources said those talks repeatedly stalled over demands that Hamas agree to disarm before Israel has fulfilled its phase one commitments. Hamas and multiple international organizations operating in Gaza have said Israel is not upholding its side of the deal, something Israel has denied while accusing Hamas of its own violations.

Israeli strikes have killed more than 765 people in Gaza since the ceasefire took effect in October, according to the Palestinian Ministry of Health.

A senior Hamas source said the militant group views the proposal as unbalanced and one that “reduces the whole process to a single clause – disarmament – while other first phase obligations are postponed or marginalized.”

“The proposed paper reflects a major imbalance in the ordering of priorities: Israel’s security first, while Palestinians’ humanitarian, political, and administrative rights are postponed,” the source said.

The source said Mladenov has taken to relaying Israel’s demands and warning that Israel will return to war if Hamas does not agree to disarm.

“It even reached the point where Mladenov conveyed veiled threats: accept the paper or face a return to war,” the source said.

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