Israeli defense officials and the Hamas rulers of Gaza said there was no formal truce in place. But the officials in Olmert's office said the prime minister had ordered the army to scale back its operations to allow Egypt to proceed in mediation talks. The officials spoke on condition of anonymity due to the sensitive nature of the talks.
CBS News correspondent Robert Berger said the de-escalation seemed to represent a "de-facto truce" between the militant Islamic group and Israel.
Heavy violence in the Gaza Strip and southern Israel has hampered U.S.-backed peace talks between Israel and the moderate Palestinian leadership of the West Bank. Olmert and Palestinian President Mahmoud Abbas have set a December target for reaching a final peace deal.
Olmert told an audience Monday that the fighting in Gaza, along with a shooting that killed eight young Jewish students at a Jerusalem seminary last week, are aimed at undermining the peace efforts.
"Their purpose is to divert us from a path of peace," Olmert said. "There's no chance that they will succeed."
Despite the violence, he added, Israel is prepared to take a "significant, important and dramatic step" to advance peace. "We will not give up on this effort," he said.
Abbas briefly called off negotiations last week in response to an Israeli military operation in Gaza in which more than 120 Palestinians were killed, including dozens of civilians, according to Palestinian medical officials. The offensive was launched in response to intense Palestinian rocket attacks on southern Israel.
Berger reports that Israeli officials seem to believe Hamas got the message.
With U.S. backing, Egypt has been trying to mediate a truce between Israel and Hamas. Officials from the warring sides have both traveled to Egypt in recent days to discuss the matter.
Hamas spokesman Sami Abu Zuhri said Monday that no comprehensive cease-fire had been reached. But Hamas officials have said in recent days that Hamas will stop the fire if Israel halts its military operations - mirroring a remark by Olmert Wednesday that Israel has no reason to attack Gaza if the rocket launchings cease.
Israeli Defense Minister Ehud Barak said there was no truce and suggested the current calm was fragile.
"There is not at this point any agreement," Barak said. "We won't complain about every quiet day but any moment we will need to act, we will."
Hamas officials said their leaders would talk to Egypt in the next day or two to continue the efforts to work out a deal. However, an informal truce already appeared to be in effect.
The Israeli army said it has not carried out air strikes or land operations in Gaza since last Wednesday. Rocket fire fell significantly over the weekend. The army said two rockets were fired Sunday, down from a daily average of more than a dozen the previous week.
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 build 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.