President Biden said Tuesday that cease-fire talks were “in the hands of Hamas right now,” and a Hamas leader in Lebanon appeared to publicly reject the deal, insisting that Israeli hostages would be released only after a cease-fire was in place and Israeli forces have withdrawn, a condition Israel has rejected. But the militant group signaled on Wednesday in a statement that it was still open to negotiations “until an agreement is reached that realizes our people’s interests and demands.”

Nidal Kuhail, 29, a resident of Gaza City who is sheltering in Rafah, said people were closely monitoring their phones and radios for updates on the negotiations, but were growing tired of waiting day after day without a breakthrough.

“We’re oscillating between being happy and then frustrated,” said Mr. Kuhail. “This seesawing in news reports has made the people incredibly confused.”

Those fluctuations have been going on for months, as a series of talks have led to no relief since a seven-day cease-fire in November.

In early February, when reports suggested that Hamas and Israel were nearing a deal, a celebration erupted in the Kuwait Specialty Hospital in Rafah, with people whistling and applauding, said Omar al-Najjar, a volunteer medical intern there.

“The atmosphere was upbeat,” said Mr. Najjar, 24. “People could finally see the light at the end of the tunnel.” But the next morning, newer reports showed that the parties will still far from overcoming their differences, casting a depressed mood across the hospital, he said.

Mr. Najjar said hopes for a cease-fire had been dashed so frequently that many were no longer paying attention to the news. “People have completely lost hope,” he said.

Over the past couple of days, the saga played out again. Arabic news outlets reported “significant progress” only to speak of “difficulties” a day later.

Hazem Surour, 20, originally from northern Gaza, said he had stopped letting news reports get his hopes up after months of Israel and Hamas failing to achieve a deal.

“We seriously need something real, not news reports,” he said. “We can only be patient and pray.”