Their first telephone conversation in more than five weeks could help put peacemaking back on track after a surge of violence that damaged hopes stirred by Israel's 12 September withdrawal from Gaza to end 38 years of military rule.
Abbas called Sharon with greetings for the Jewish New Year, which starts at sundown on Monday. Sharon expressed best wishes for the Muslim holy month of Ramadan, starting this week.
A statement from Sharon's office said they "agreed to tighten cooperation between them and to work together to advance the process. They also agreed to meet soon in order to advance various issues that are on the agenda".
"Both leaders expressed hope that the new year would be more successful, a year of peace and hope," it said.
Israeli and Palestinian officials said no date had been set for a summit.
Israel says it has suspended air raids, targeted killings and artillery fire in the Gaza Strip and West Bank until further notice.
Saeb Erikat: A cooldown is in the
interests of both sides
"We have decided to suspend the offensive operations that we launched last week in response to rocket fire from the Gaza Strip into southern Israel," an official in Prime Minister Ariel Sharon's office said on Sunday.
The decision means the suspension "for now" of Israeli air raids in the Gaza Strip, of artillery fire towards the north of the territory and of operations aimed at eliminating resistance groups in Gaza and the West Bank, said the official, who declined to be named.
The declaration was welcomed by the Palestinian Authority, which said it would increase the chance for progress in the peace process.
"A cooldown between the Palestinians and Israelis is in the interests of both sides,"
Sami Abu Zuhri (R): The move is
a ploy to divide Palestinians
Chief Palestinian negotiator Saeb Erikat told AFP.
"Such a cooldown will help us return to the peace process with real meaning."
Hamas, however, dismissed the move as a ploy to split the Palestinian people.
"This statement is part of the propaganda campaign to blackmail our people and to put pressure on the Palestinian Authority to fight against the factions and resistance groups," said spokesman Sami Abu Zuhri.
Also on Sunday, Israel Radio reported that an Israeli regional commander had found soldiers who shot and killed a Palestinian youth at fault since their lives were not endangered.
In the incident on Friday, Palestinians said the 13-year-old boy was killed by soldiers when he threw stones at them in the West Bank city of Nablus.
Israeli commander: Soldiers used
excessive force in Friday's killing
The troops said they believed the boy was holding a gun, the radio said.
A preliminary investigation by the commander of the area found that the soldiers acted with excessive force when they shot at the youth, according to the report.
The findings will be passed on to senior army commanders who will decide whether to open a formal investigation against the troops, the radio said.
The officer who oversaw the soldiers deployed in the area at the time has been removed from operational duty, the radio added.
Israel urged its citizens on Sunday to avoid going on holiday in Egypt's Sinai resorts, citing intelligence warnings that they could be abducted by pro-Palestinian militants during Jewish holidays.
Thousands of Israelis ignored a similar advisory last year ahead of attacks on several Sinai resorts.
Egypt says there was no foreign
involvement in the Sinai blasts
Danny Arditi, Sharon's top counter-terrorism adviser, said the latest warning was "really a pinpoint alert".
"The target is the coastal area where Israelis stay. It [the threat] is against Israelis who come to celebrate the High Holy Days," he told Israel Radio. The holidays last for about three weeks from 3 October.
Israel's Maariv newspaper said the Mossad spy service had received word of a Palestinian cell in Sinai which, backed by Lebanese Hizb Allah fighters, planned to abduct Israeli tourists and trade them for Palestinians jailed in Israel.
Arditi confirmed that hope of a prisoner swap was believed to be a factor in a plot that he said involved Palestinians and others.
There was no immediate Egyptian comment on the alert.