Hebron - holy to Muslim and Jew - has long been a flashpoint
The Israeli and Palestinian prime ministers have met for the first time against a background of further violence in the West Bank and Gaza Strip.
The new Palestinian Prime Minister, Mahmoud Abbas - better known as Abu Mazen - was expected to discuss the US-backed peace plan, known as the roadmap, with Ariel Sharon.
It was the first such summit since the current Palestinian intifada erupted in September 2000 but there was no word on any progress in the three-hour meeting.
As Abu Mazen travelled to meet the Israeli leader for the first time in his new official capacity, a suicide bomber killed two Jewish settlers in the West Bank city of Hebron.
The Palestinian bomber, who was disguised as a religious Jew, also blew himself up, the Israeli army said.
Later, there were reports of a Palestinian gunman opening fire in a Jewish settlement in the West Bank injuring one resident.
In further violence on Saturday, Israeli soldiers shot and killed an armed Palestinian and wounded nine others during clashes in Beit Hanoun, in the Gaza Strip.
Veteran negotiator pulls out
On the eve of the meeting, the top Palestinian negotiator, Saeb Erekat, announced his resignation after apparently being excluded from the talks team.
Mahmoud Abbas: Committed to disarming the militants
The Palestinians have accepted the roadmap in its current form, while Israel has so far refused to do so, outlining more than a dozen reservations.
The BBC's James Reynolds in Jerusalem says the meeting is taking place under great pressure from the Bush administration.
There is plenty for the sides to talk about, but no-one is expecting any great breakthroughs, our correspondent says.
Abu Mazen is expected to ask Mr Sharon to accept without reservation the roadmap, under which a Palestinian state would be established by 2005.
However, Mr Sharon wants first to see the Palestinians tackle armed groups responsible for suicide attacks - an issue which is expected to be his main topic of conversation at Saturday's meeting.
Mr Sharon is due to go to Washington to discuss the roadmap with President George W Bush on Tuesday.