As international negotiators discussed a cease-fire in the Gaza Strip on Monday, officials and analysts said there was little expectation that Israel and Hamas would agree to a truce before the American presidential election next Tuesday.

Envoys from Israel, Egypt, the United States and Qatar took part in the cease-fire talks in Doha, the Qatari capital. American mediators were also expected this week to push for a truce between Israel and Hezbollah in Lebanon.

But a senior Hamas official has already rejected the premise of a 48-hour cease-fire in Gaza — an idea Egypt proposed over the weekend — during which the group would release four Israeli hostages in exchange for Palestinians imprisoned in Israel.

The official, Osama Hamdan, said on Sunday that Hamas would agree only to a permanent cessation of hostilities, dashing hopes that Israel’s recent killing of the group’s leader, Yahya Sinwar, might bring about a swift change in its negotiating position.

Prime Minister Benjamin Netanyahu’s office said on Monday evening that Israel’s chief envoy, David Barnea, the head of the foreign intelligence service, had returned from Doha after meeting with the C.I.A. director, William J. Burns, and the Qatari prime minister and foreign minister, Mohammed bin Abdulrahman Al Thani.

The parties discussed a “new and unified framework” for a cease-fire and planned “in the coming days” to discuss the feasibility of further talks to advance a deal, Mr. Netanyahu’s office said.