A sense of urgency hung over the meeting.

The Qatari prime minister sat across from Hamas’ chief negotiator, Khalil Al-Hayya, under the maroon-and-white flag of the Gulf nation on Monday evening. The two had met many times before in talks that often proved fruitless.

But this time was different.

The United States had just put forward a new ceasefire proposal that could end the nearly two-year war in Gaza. And Sheikh Mohammed bin Abdulrahman bin Jassim Al-Thani was pressuring Al-Hayya to accept.

The discussion wrapped up shortly before 9:30 in the evening, according to a source familiar with the meeting, but the real work was just beginning. After Al-Hayya left, Qatari negotiators got on the phone with their Israeli counterparts to update them on the nascent ceasefire effort.

Unlike mo

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