SHARM EL SHEIK, Egypt – In a crucial step heralded as a fresh start to peacemaking, Prime Minister Sharon and Palestinian leader Mahmoud Abbas promised yesterday to halt all acts of violence and agreed to meet again soon to tackle the tougher issues that for decades have blocked the road to peace.

Even if their cease-fire pledge sticks, much negotiating lies ahead as the two sides work to rebuild the trust destroyed in four years of deadly attacks.

“What we agreed upon today is simply the beginning of the process of bridging the gap,” Mr. Abbas said after his first face-to-face meeting with Mr. Sharon since succeeding Yasser Arafat. The Palestinian leader made clear the two sides have yet to wade into fundamental issues, including control of Jerusalem and “the settlements, the release of prisoners, the wall.”

The speeches by the two leaders at this Egyptian resort, broadcast live on Israeli and Arab TV stations, were greeted with a mixture of hope and skepticism on a cold, rainy day back home. Many people said they would settle for modest improvements in their daily lives.

“We’ve gone from euphoria to extreme disappointment,” said an Israeli law student, Shimrit Golan, who lives in Jerusalem. “We’ll wait and see what happens.”

The terrorist group Hamas threw up an immediate roadblock, saying it was waiting to hear from Mr. Abbas and to see what Israel would do before committing to a halt in violence.

Yet the verbal cease-fire pledge and the sight of Mr. Abbas and Mr. Sharon grinning broadly as they shook hands across a summit table were the clearest signs yet of a new life for the peace process after Arafat’s death in November and Mr. Abbas’s election in January.

One Israeli official, Gideon Meir, said “there was a great atmosphere in the talks … smiles and joking.” In another sign the talks went well, Egypt and Jordan announced they would return their ambassadors to Israel after a four-year absence – possibly within days.

Emerging from private talks, Mr. Sharon promised that the Israeli military would stop attacks on Palestinian Arabs, and Mr. Abbas promised a halt to terrorist attacks on Israelis.

“We must move forward cautiously,” Mr. Sharon said. “This is a very fragile opportunity that the extremists will want to exploit. They want to close the window of opportunity for us and allow our two peoples to drown in their blood. … If we do not act now, they may be successful.”

In the first reported violation of the cease-fire, Palestinian Arabs shot at a car near a West Bank Jewish settlement after nightfall and fired and threw firebombs at soldiers who came to investigate. No one was hurt. The Al Aqsa Martyrs Brigade, affiliated with Mr. Abbas’s Fatah movement, claimed responsibility.