(Adds Egypt working on truce proposal)

By Sue Pleming and Dan Williams

JERUSALEM, March 5 (Reuters) - Israel and the Palestinians agreed to resume peace talks on Wednesday under pressure from U.S. Secretary of State Condoleezza Rice, but progress appeared to hinge on stemming bloodshed in the Hamas-run Gaza Strip.

Signalling a willingness by Israel to hold fire after a Gaza offensive that killed more than 125 Palestinians and stalled negotiations, Prime Minister Ehud Olmert said there would not be further such attacks if Palestinian rocket salvoes were to stop.

Rice ended a three-day troubleshooting visit in the region by dispatching an envoy to Cairo, a key player in trying to broker any calm between the Jewish state and Islamist Hamas.

Hamas's Western-backed rival, Palestinian President Mahmoud Abbas, had said he would not return to statehood talks with Olmert until Israel reached a ceasefire in Gaza. Palestinian officials said Egypt would present a truce proposal next week.

Rice, her own credibility on the line, thought early on Wednesday she had a deal with Abbas but, on hearing news reports his participation was still conditional, interrupted lunch with Israeli Foreign Minister Livni to call him for clarification.

"I talked directly with President Abbas. He said there was not to be a condition," Rice told reporters traveling with her after she left Israel for a NATO meeting in Brussels.

Only after speaking to Abbas for a second time did she feel confident to make the announcement at the news conference.

"I do understand the difficult circumstances for President Abbas but I think he has made the right decision," said Rice.

Rice did not say when the next round of talks would be held. The United States hopes negotiations could result in an accord before U.S. President George W. Bush leaves office in January.

Israel called its five-day Gaza sweep, half of whose Palestinian victims were identified by hospitals as civilians, a response to rocket strikes by Hamas. A rocket killed an Israeli civilian last week and two soldiers died fighting Gazan gunmen.

Olmert told reporters on Wednesday after meeting Rice: "One thing should be clear: If there is no Qassam (rocket) fire on Israel, there will be no Israeli attack on Gaza. We do not rise in the morning and think about how to attack Gaza."

HAMAS COOL ON OVERTURE

Hamas was cool to Olmert's overture, though its rocket fire has largely abated since Israeli troops withdrew on Monday.

Another militant group, Islamic Jihad, fired several rockets on Wednesday, calling them retaliation for a Israeli commando raid on Gaza overnight. No one was hurt by the salvo.

"We want deeds, and not words. There must be a total cessation of all forms of Israeli aggression on our people, in addition to a reopening of all crossings," Hamas official Sami Abu Zuhri told Reuters, referring to an Israeli-led blockade on Gaza, most of whose 1.5 million Palestinians are aid-dependent.

Abbas's office issued a statement after he spoke to Rice that did not repeat his condition for talks. It said Rice was exerting efforts to "enforce a mutual calm" and Abbas's intention was to resume the peace process and negotiations.

Palestinian officials said Egyptian mediator Omar Suleiman would present Israel and Hamas with a truce proposal including a mutural cessation of hostilities and Israel's assent for key border crossings to open. Suleiman is due in Israel next week.

Rice said a special U.S.-Israeli-Palestinian committee, led by U.S. Gen. William Fraser, would meet next week to examine to what extent the sides were meeting their commitments under a long-stalled peace "road map."

The U.S. general has already delivered a preliminary report to Rice on the performance of both sides. "I expect that he (Fraser) will clearly talk directly with them on what needs to be done and ways to get it done," said Rice.

The Palestinians had sought such a meeting to put pressure on Israel to meet its obligation to freeze settlement activity. The road map calls on Palestinians to rein in militants.

At her news conference, Rice said she was sending David Welch, the U.S. assistant secretary for Near Eastern affairs, to Cairo, which European Union officials regard as key to brokering a ceasefire and the reopening of Gaza's border with Egypt.

Welch, she said, would discuss with the Egyptians "the entire situation" in the Gaza Strip.

Cairo also has been trying to mediate between Israel and Hamas on exchanging an Israeli soldier seized by the Islamist group in 2006 for hundreds of Palestinians jailed in Israel. (Additional reporting by Adam Entous in Jerusalem, Ali Sawafta and Wafa Amr in Ramallah and Nidal al-Mughrabi in Gaza, Writing by Dan Williams and Jeffrey Heller in Jerusalem; Editing by Robert Woodward)

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