High-level Israeli and Palestinian officials have met in Jerusalem in the presence of a US envoy.
The Israeli army destroyed buildings in the Gaza Strip overnight
US State Department official David Satterfield "underscored security steps the Palestinians must make to end terror and violence", an official said.
Talks - attended by donor organisations - also looked at ways to improve conditions for Palestinians.
Just before the meeting Israeli troops shot dead two unarmed Palestinians trying to cross from Gaza into Israel.
The men were part of a group of six, one of whom was captured, Israeli military sources said.
The other three escaped and a search for them has been launched.
It is not clear if they were militants or if they were seeking work in Israel.
Dov Weisglass, Sharon's chief of staff, led the Israeli team and Palestinian chief negotiator Saeb Erekat headed the
Palestinian delegation, political sources said.
Israeli sources said talks were intended to pave the way for talks between Mr Sharon and Palestinian Prime Minister Ahmed Qurei.
But Palestinians said they wanted to focus on the US-backed "roadmap" peace plan.
"The good thing is that the two sides are talking," a Western diplomat was quoted by Reuters as saying, although the diplomat added that expectations for significant
progress were low.
Erekat spoke to a Sharon envoy
Israeli closures of Palestinian territories have caused severe economic hardship, cutting Palestinians off from the Israeli economy which provided them jobs before the latest uprising began three years ago.
"They discussed permits, they discussed checkpoints, closures,
movement in general for Palestinians, as well as the ideas that the
Israelis have," State Department spokesman Richard Boucher said.
Israel says the closures are necessary to prevent militant attacks on Israelis, but critics says they constitute collective punishment.
Israeli forces raided a refugee camp in the southern Gaza Strip overnight.
They destroyed a number of buildings near the town of Khan Younis.
Palestinians said the structures were homes. Israel said they were abandoned and used "by Palestinian terrorist cells to launch mortar bombs and fire missiles" at Israeli targets.
Two Israeli soldiers were lightly injured in the raid, the military said.