Sharm el Sheik, Egypt ? In a crucial step heralded as a fresh start to peacemaking, Israeli Prime Minister Ariel Sharon and Palestinian leader Mahmoud Abbas promised Tuesday 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,” Abbas said after his first face-to-face meeting with Sharon since succeeding Yasser Arafat.

The militant group Hamas threw up an immediate roadblock, saying it was waiting to hear from 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 Abbas and 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 Abbas’ election in January.

Emerging from private talks, Sharon promised that the Israeli military would stop attacks on Palestinians, and Abbas promised a halt in militant attacks on Israelis.

In the first reported violation, Palestinians 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’ Brigades, affiliated with Abbas’ Fatah movement, claimed responsibility.

Israeli Prime Minister Ariel Sharon, right, and Palestinian Authority President Mahmoud Abbas, left, also known as Abu Mazen, shake hands prior to their delegations' meeting Tuesday at the Red Sea resort of Sharm el-Sheik, Egypt.

In one of the most symbolic gestures out of the summit, Sharon invited Abbas to visit him at his ranch in Israel and Abbas accepted, Meir said.

Palestinian Foreign Minister Nabil Shaath said the visit would take place soon and be followed by other meeting. Talks by lower-level officials were to resume today.