DOHA, Qatar—The chief brokers of the Israel-Hamas hostage-prisoner exchange are pushing the two sides for a long-term cease-fire that would prolong the truce in Gaza beyond the current two-day extension and start talks that would end the war altogether, said Egyptian and Qatari officials.

A long-term cease-fire would likely require Israel and Hamas to make hard-to-swallow concessions, such as trading Israeli soldiers for potentially thousands of Palestinian prisoners in Israeli jails, the officials said. And it would require Israel to hold back on an offensive in southern Gaza intended to capture the strip and kill Hamas’s top leadership, the officials said. Hamas could also have to accept demilitarization, they added.