A senior Israeli Defense Ministry official, Amos Gilad, returned Sunday from talks in Cairo.
Since Israel and Hamas refuse to speak directly to each other, any understanding would not be put in writing, defense officials said. Israel and Hamas have reached informal truces in the past, though the arrangements have unraveled.
Hamas seized control of Gaza last June from Abbas' forces. Since then, Israel has pursued peace efforts with Abbas, who rules from the West Bank, while battling Hamas in Gaza both through military operations and an economic blockade on the area.
The cease-fire efforts reflect the growing recognition of Hamas' ability to upset the peace talks.
A Hamas official responsible for talks with Egypt, Ayman Taha, said Monday the recent drop in rocket fire was part of Hamas' "field tactics," but did not stem from any understanding.
Hamas will not reach any agreement with Israel until it opens Gaza's border crossings, Taha said. Israel has in recent months prevented all except basic necessities from entering the territory, where 1.4 million Palestinians live, as part of efforts to get Hamas to stop the barrages.
Also Monday, Israel lifted a closure it imposed last week after the shooting on the Jewish religious school.
The measures, which barred most Palestinians from entering Israel, was canceled "following security assessments," the army said.
The gunman who carried out the attack last Thursday was a Palestinian from east Jerusalem, an area under Israeli sovereignty. But Israeli officials suspected the man was assisted by West Bank militants. The gunman was shot and killed at the scene.
In another possible complication for peace efforts, Israeli officials said 400 new homes would be built in the Neve Yaakov neighborhood of disputed east Jerusalem. The plan is awaiting approval of a planning committee, said Ariela Smilinski Deri, a spokeswoman for the Jerusalem municipality.
On Sunday, Israel said it would build 350 apartments in a West Bank settlement, and 750 homes in another east Jerusalem neighborhood.
The plans drew condemnations from the Palestinians, who hope to make east Jerusalem the capital of a future independent state.