TEL AVIV—Secretary of State Antony Blinken urged Israeli leaders to extend a pause in their combat operations against Hamas militants in Gaza, which is teetering after a one-day extension was clinched following all-night negotiations.

As the temporary truce was set to expire Thursday morning, Qatari mediators announced that the parties had agreed to extend it by one more day. By late Thursday afternoon, Hamas released two hostages, identified by the Israeli government as Mia Shem and Amit Soussana, and was expected to release further hostages later in the evening. But ongoing negotiations for a further extension of the cease-fire beyond Friday morning face an uphill battle, said Egyptian and Qatari officials involved in the talks.