Under the terms of the cease-fire, Israel is seeking international and regional guarantees that Hamas cannot rearm, and the Palestinians want Israel to end its blockade of the aid-dependent territory, Reuters reported.
Hamas officials, meanwhile, said they were still considering the plan, despite earlier reports that they had rejected it.
Once an agreement is reached, Israel is expected to end its military campaign in Gaza, but in the meantime it could expand its ground operation. And once Israel pulls out, Egypt and other Arab states would get Hamas to stop firing rockets into Israel, according to diplomatic and political sources, reported Reuters.
As the talks were taking place in Cairo, the U.N. Security Council appeared close to voting on a resolution that called for an immediate cease-fire by both sides, according to Arab diplomats, the New York Times reported.
The latest resolution specifically mentions Hamas, whereas earlier versions referred to a cessation of rockets without specifying which side was firing them.
Also Thursday, the U.N. Relief and Works Agency said it was halting food deliveries into Gaza after one of its contract drivers was killed by Israeli tank fire at a border crossing.
"We've been coordinating with them (Israeli forces) and yet our staff continue to be hit and killed," said U.N. spokesman Chris Gunness, quoted the Associated Press.
The attack at the border crossing followed an incident where Israel fired shells at a target next to a U.N.-run school where Gazans had sought refuge, killing nearly 40 Palestinians.
Israel said militants had launched an attack from the area, and then ran into a crowd of civilians for cover. The United Nations has demanded an investigation.
Since the Dec. 27 offensive against Hamas began, about 11 Israelis have died and 750 Palestinians -- roughly half of which are believed to be civilians -- have been killed, according to Palestinian hospital officials and human rights workers, the AP reported.
Word of the U.N. suspension of aid deliveries came after several rockets were fired from Lebanon and landed in northern Israel, raising concerns that they could represent a broadening of the conflict. But Israeli and Lebanese governments played down their significance, according to the New York Times.