Senior government sources said on Monday evening that confidants of Prime Minister Ehud Olmert and Palestinian Authority Chairman Mahmoud Abbas were in "constant contact" trying to reach an agreement to expand the agreement to include the West Bank.
The comments came hours after Olmert, in a speech at David Ben-Gurion's grave in Sde Boker marking the 33rd anniversary of his death, defined the concessions Israel would be willing to make were the Palestinians to end terrorism, give up demands for a right of refugee return and free captive soldier Cpl. Gilad Shalit.
Echo Olmert's offer (editorial)
The comments also came hours after two Kassam rockets were fired at the Western Negev, yet again shattering the cease-fire.
Nevertheless, during his speech at Sde Boker, Olmert expressed hope that the Gaza cease-fire agreement would be the start of a much wider process.
"I come today, from here, near the tomb of David Ben-Gurion, to suggest to you a different path," he said, addressing the Palestinians, "a path that offers a chance for a different future, for you and for us. We started it the day before yesterday."

PM Ehud Olmert. Happy to extend his hand in peace to the Palestinians.
Photo: AP , AP
Both Olmert's and Abbas's staffs were exploring ways to expand the agreement to include the West Bank, government officials said. They added that it was easier to deal with the Palestinians on this issue than on the release of Shalit, because the decision to free Shalit needed the approval of Hamas's Damascus-based leader Khaled Mashaal, while cease-fire issues needed PA Prime Minister Ismail Haniyeh's okay.
According to these officials, since Haniyeh lives in Gaza and is in touch with the daily plight of the people there, he was more apt to want to take actions that could alter the difficult situation on the ground.
Officials in the Prime Minister's Office said Olmert's decision to directly address the Palestinian people and say he would release numerous Palestinian prisoners, "including ones who were sentenced to lengthy prison terms," was meant to go over Mashaal's head and tell the Palestinians that Mashaal was the obstacle standing in the way of a reunion with their relatives.
"I hereby declare that when Gilad Shalit is released and returned to his family, safe and sound, the government of Israel will be willing to release numerous Palestinian prisoners - including ones who were sentenced to lengthy prison terms - to increase the trust between us and prove that our hand is truly extended in genuine peace," Olmert said.
"I said it before Gilad Shalit was abducted, and I have not changed my position," he added. "I know that many Palestinian families yearn for the day when their loved ones will return home. This day could be very close."
The unstated subtext, a senior official in the Prime Minister's Office said, was that Mashaal was keeping this from happening.
The official also said Olmert would be willing to release a large amount of prisoners, "larger than they probably think."
Olmert, in his speech, laid out a far-reaching vision of peace on Monday, reaffirming that Israel would be willing to withdraw from a great deal of territory in return for peace.
"I extend my hand in peace to our Palestinian neighbors, hoping that it will not be rejected," he said. "We, the State of Israel, will agree to withdraw from a large amount of territory, and from the settlements that we established there - something that is very difficult for us, akin to the parting of the Red Sea - but we will do that in exchange for real peace.
"You must stop the terrorism, violence and efforts to harm Israeli citizens in the South, center and North, recognize our right to live in peace and security next to you and relinquish your demand for the realization of the right of return," he said, directly addressing the Palestinians.
While speaking of a willingness to withdraw from West Bank territory, Olmert made no reference at all - as he did before the election campaign and in the months leading up to July's war in Lebanon - to doing so unilaterally as part of a "realignment" plan. On Monday he was speaking of a process that would come out of negotiations and the road map.
The prime minister said that if a new PA government accepted the Quartet's conditions for legitimacy, implemented the road map and released Shalit, he would suggest a meeting with Abbas to conduct a "true, open and serious" dialogue.
Olmert said that within this framework and in line with the road map, the Palestinians could establish an independent, viable state with contiguous territory in the West Bank, and have full sovereignty over recognized borders.
He also said that within this framework, Israel's borders would be established and "would be different from the territory that is now under Israel's control."
In a somewhat new twist, Olmert said Israel would "seek the assistance of those neighboring Arab states that strive for a peaceful solution to the conflict between us, including Jordan, Egypt, Saudi Arabia and the Gulf States, to benefit from their experience and receive backing for direct negotiations between us."
This is the first time he has mentioned enlisting the help of neighboring Arab states in negotiating with the Palestinians, with Israel's position in the past being that it preferred direct bilateral negotiations with the Palestinians.
"The voices emanating from those states regarding the need for recognition and normalization of relations with the State of Israel - including, for example, some parts in the Saudi peace initiative - are positive, and I intend to invest efforts to advance the connection with those states and strengthen their support of direct bilateral negotiations between us and the Palestinians," Olmert said, in one of the rare instances that he has publicly acknowledged something positive in the Saudi diplomatic initiative from 2002.