"There's an attempt to get the peace process back on track in a bid to make the withdrawal from Gaza, if it happens, a serious, real (and) practical step," Qureia told reporters before he walked into talks with Peres at a meeting room at a Dead Sea resort.
He said he hoped that the pullout will be in implementation of the road map, an internationally backed peace plan that calls for an end to Palestinian-Israeli violence and the creation of an independent Palestinian state.
Earlier, Peres said the Gaza fighting was sparked by Hamas and expressed hope that both sides would overcome the violence.
"It was a protest by Hamas against the Palestinian Authority," Peres said of the flare-up. He said Hamas apparently was trying to respond to re-elections in certain Palestinian areas called for by the Palestinian Authority.
"I hope we shall overcome it," Peres said. "We do not want to escalate."
Asked how Israel will respond to the clashes, he said: "With great restraint."
In Egypt, visiting Palestinian President Mahmoud Abbas said the Gaza violence was subsiding.
"I think that the situation has begun to come under control in Gaza. That's why this will not have any negative impact on my visit to America," Abbas said, referring to his 26 May audience with US President George Bush.
Peres said he and Qureia were in constant contact about the Gaza withdrawal and accompanying economic and social issues.
He said both sides had issues to discuss related to the aftermath of the pullout. "To prepare for after the withdrawal, we have to start now," he said. He said his talks with Qureia were more than coordination.
"We don't want to create an impression that we are playing a role in the Palestinian elections"
Israeli vice prime minister
"It's planning. It's very complicated. There are a lot of details," he added.
He said he hoped that Israel's pullout from Gaza would take place as scheduled in August. "Any (further) delay will endanger the whole process," Peres said.
Asked about the strong showing Hamas is expected to make against Abbas's Fatah movement in the parliamentary Palestinian elections scheduled for mid-July, Peres said: "Clearly this is a problem."
"But we don't want to intervene. We don't want to create an impression that we are playing a role in the Palestinian elections," he said.
The two were meeting at the World Economic Forum in Jordan, attended by about 1300 business and political leaders.