Security officials are expected to advise the cabinet Sunday not to expand the Gaza Strip cease-fire to the West Bank, Israel Radio reported Friday.

U.S. Secretary of State Condoleezza Rice, who met with Prime Minister Ehud Olmert on Thursday, expressed her appreciation for the restraint Israel has exercised in recent days in the face of continued rocket fire from the Gaza Strip and said the cease-fire in Gaza needs to be bolstered with further measures.

Foreign Ministry spokesman Mark Regev told reporters Thursday that Olmert wants to extend the cease-fire to the West Bank once it has proven effective in the Gaza Strip. As of Friday morning, Palestinians have fired 14 Qassam rockets on Israel since the cease-fire went into effect Sunday, according to the Israel Defense Forces.

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Political officials told Israel Radio that IDF arrest raids in the West Bank are meant to stop bombings that, unless they are stopped in time, tend to be far more deadly than the rocket fire coming from Gaza. The officials said that even a brief cease-fire in the West Bank would just give Palestinian militants a chance to build up the terror infrastructure there.

In the past year, 33 people have been killed in Palestinian attacks on Israel, of whom only five were killed by attacks from Gaza, Israel Radio reported.

Meretz-Yachad chairman Yossi Beilin said Israel should not accept what he characterized as the security establishment's automatic rejection of a truce and should make every effort to expand the cease-fire, Israel Radio reported.

Rice said after her meeting with Palestinian Authority Chairman Mahmoud Abbas on Thursday that Israel and the Palestinians should step up efforts to revive peace talks and move toward a solution to the Israeli-Palestinian conflict.

"Hopefully we can take this moment to accelerate our efforts and intensify our efforts toward the two-state solution that we all desire," Rice said at a news conference with Abbas.

Rice commended Olmert for his address earlier this week at a memorial event for Israel's first prime minister, David Ben-Gurion, at his burial site in Sde Boker.

"The speech will contribute to calm and will further the peace process in the region," sources in the Prime Minister's Office quoted the visiting American official as saying.

Olmert said in the Sde Boker speech that Israel would accept a territorially contiguous Palestinian state in the West Bank in exchange for Palestinians relinquishing their demand for a return of Palestinian refugees to Israel.

During his meeting with Rice, Olmert updated her on the talks held a day earlier with visiting Egyptian intelligence chief Omar Suleiman regarding efforts to gain the release of abducted Israel Defense Forces soldier Gilad Shalit.

Rice informed Olmert of the content of her talks earlier in the day with Abbas. Following her meeting with Olmert, Rice met with Foreign Minister Tzipi Livni.

Like Rice, Abbas also had good things to say about the speech Olmert made at Sde Boker.

"In the meeting with the secretary of state we discussed the cease-fire, and we hope that we can return to the Sharm el-Sheikh understandings [which included the release of prisoners and an IDF pullout from West Bank cities]," Abbas said, "in order to bring about the resumption of the diplomatic process and the implementation of the road map."

During the meeting Abbas recommended that any future negotiations between Israel and the Palestinians be held along two tracks - one dealing with day-to-day problems and the other with political issues.

Standing alongside Abbas, Rice addressed aspirations for a Palestinian state.

"The United States has made clear that we expect it to be a viable and contiguous state when it is created," she said. "Secondly, that no actions that are being taken now should prejudge the outcome of a final status agreement. That means very clearly that if actions are being taken now, they will not be considered by the United States to prejudge the outcome of final status."

However, one Palestinian source who attended the Rice-Abbas meeting sought to underplay the significance of the discussion.

"Rice asked to receive updates and she got them," he said. "It is difficult to say that we reached a specific point [in the meeting]. Abu Mazen [Abbas] explained to her that at this moment there is no progress in the matter of the unity government and if the Hamas stance remains unchanged, it is possible that in two or three months we will have to go to early elections."

The same source said Hamas was very pleased with Palestinian Prime Minister Ismail Haniyeh's reception in Egypt, his first stop in his first trip abroad since Hamas won the national elections in the Palestinian Authority earlier this year.

"They are sure that the international boycott on the Palestinian Authority is about to be lifted," said the source. "In addition, they are hoping to complete a deal for the release of soldier Gilad Shalit and thus score points in their favor among the Palestinians."