At his seaside office complex in Doha on Wednesday evening, the Qatari prime minister thought he had a deal. Hamas’ negotiators, led by a burly former lawmaker, had left the prime minister’s office, having given up on an eleventh-hour demand that was the last major obstacle to a ceasefire in the Gaza Strip after 466 days of war.

Reporters had begun to assemble in an auditorium downstairs, expecting to witness the prime minister, Sheikh Mohammed bin Abdulrahman Al Thani, announce that he and other mediators had finally brokered a deal. Two American envoys joined Sheikh Mohammed as he prepared his statement.