Sharon’s office put out a statement saying the talks were over, and Abbas’ convoy was seen racing away from Sharon’s residence in Jerusalem.
There were no immediate details on the outcome of the meeting, although Channel 2 TV said the atmosphere was tense.
Abbas was heading back to Ram Allah in the West Bank to give a news conference.
The meeting was meant to step up coordination of Israel’s planned withdrawal from the Gaza Strip, which is scheduled to begin in less than two months.
But a recent spike in violence threatened to cloud the gathering.
Early on Tuesday, Israel arrested more than 50 Islamic Jihad activists and said the ceasefire would no longer apply to the group following a series of attacks.
The summit follows a weekend visit by US Secretary of State Condoleezza Rice, who urged both sides to step up cooperation to ensure a smooth pullout.
“In some ways from Sharon‘s perspective it’s like punching a clock,” Israeli political analyst Yossi Alpher said of the summit.
“The Americans insisted this happen, so he’s doing it. I don’t think the reality will be very different after the meeting.”
The reality on Monday, however, was a bloody one. In the third attack in three days by Islamic Jihad, armed men in the northern West Bank ambushed an Israeli minivan, killing one passenger and wounding another.
Israeli soldiers killed a Palestinian and wounded another as they tried to scale a fence from Gaza into Israel, Palestinian hospital officials said.
“We assert our commitment to the truce, and we hope that the most recent events will not affect the meeting between Abbas and Sharon”
While fighters argued the rising violence did not signal the collapse of a ceasefire agreed to in February, the bloodshed has soured the atmosphere.
On Monday, Palestinian Foreign Minister Nasser al-Kidwa condemned the violence, saying violations by either side “do not serve the Palestinian interest”.
“We assert our commitment to the truce, and we hope that the most recent events will not affect the meeting between Abbas and Sharon,” he said.
In the months since the February talks between the two leaders in Sharm el-Shaik in Egypt, Israel has been criticised for being slow to carry out commitments to release prisoners, hand over West Bank towns and remove roadblocks that severely restrict Palestinians’ freedom of movement.
Israel says progress depends on the Palestinian Authority first reining in extremists, and the nation’s officials give Abbas low marks in that area.
Abbas has chosen persuasion over confrontation to sway his main rival, the Islamic resistance group Hamas – a strategy Israel denounces as naive and destined to fail.
Israelis say Abbas needs to do
“What we’re seeing over the last few days is very troubling,” said Israeli Foreign Ministry spokesman Mark Regev. “There’s no doubt that [Hamas] is using this as a period to regroup, rearm and retrain.”
Another Israeli official said Sharon had no intention of offering Abbas further confidence-building “gestures” at Tuesday’s meeting unless Abbas took a harder line against fighters.
The official would not allow his name to be used because of the sensitivities surrounding the summit at Sharon‘s residence in Jerusalem.
Palestinians say Israel has many shortcomings of its own to answer for, especially the continued expansion of Jewish settlements in Palestinian territory and construction of a West Bank separation barrier that the Palestinians say usurps some of their land.
Palestinian leaders insist on their right to deal with Hamas in their own way.
“We know our conditions, we know our domestic realities and we know the best ways of achieving a cessation of violence,” said lawmaker Hanan Ashrawi.
“Because if you start cracking down, imprisoning, shooting and killing, then you end up with a civil war,” she added.
“We know our conditions, we know our domestic realities and we know the best ways of achieving a cessation of violence”
Sharon was expected to concentrate on security during the summit. Officials said he would ask Abbas to explain how the Palestinian Authority planned to prevent fighters from attacking Jewish settlers and soldiers as they evacuate Gaza.
The Palestinians have drawn up a wish list of their own for after the evacuation: Assurances Gazans will have access to the West Bank, the ability to build an airport and harbour for Gaza and control over Gaza‘s border with Egypt.
Walid al-Umari, Aljazeera’s correspondent in the occupied Palestinian territories, said the Palestinian side will also demand the release of more detainees.