That optimistic forecast, only days ahead of a peace summit with Israeli Prime Minister Ariel Sharon and US President George W. Bush, came despite the hardline Islamic group Hamas vowing to continue its attacks as long as Israel fails to make substantial concessions.

Two summits slated for next week are part of efforts to end 32 months of Palestinian-Israeli bloodshed with the so-called roadmap for peace, which calls for both an end to violence and the creation of a Palestinian state by 2005.

The first will be hosted Tuesday by Egyptian President Hosni Mubarak at the Red Sea resort of Sharm el-Sheikh and will bring together Bush and a number of Arab leaders.

On Wednesday, King Abdullah II will host Bush, Abbas and Sharon in the Jordanian coastal resort of Aqaba.

"After the two summits... we will continue the negotiations with the Palestinian organizations and within two or three weeks maximum, we will succeed in having a universal agreement which we can count on," Abbas said in an interview with Israeli public television Friday night.

"I am an optimist: we will achieve an agreement on a halt in the violence," he said.

Abbas also said the Palestinian security services would be ready in about the same amount of time to take responsibility for certain areas of the Gaza Strip and West Bank where Israeli troops have taken control.

"We're talking about 'Gaza First,' and certain cities in the West Bank. We will take responsibility for the security (in these areas) in two to three weeks," he said.

Abbas had met with Sharon late Thursday in Jerusalem office for the second time in two weeks to discuss kickstarting the roadmap.

In line with the plan's call for Israeli troops to withdraw to positions they held before the uprising broke out, Sharon agreed to a phased handover of security control in Gaza and West Bank towns.

In return, Sharon has demanded Abbas move to halt the violence, including "dismantling terror organisations, confiscation of illegal weapons and the ending of incitement."

If the Palestinians cracked down on their radical groups, Sharon vowed he would begin political negotiations on the establishment of a Palestinian state.

In his interview, Abbas said: "I believe that both parties understand that the only way to peace is negotiation. The other means don't help."

He added that he believed the Palestinian territories needed "one sole authority and one sole legal armed force."

The comment was probably aimed at Hamas, which warned Friday it would only stop its suicide attacks if Israel halts all "aggression" against the Palestinians.

Meanwhile, Israelis and Palestinians will craft a joint statement Saturday to be released at the close of next week's three-way summit of US, Israeli and Palestinian leaders, Palestinian sources said.

The sides agreed to draft the statement at the Thursday night meeting between Israeli Prime Minister Ariel Sharon and his Palestinian counterpart, Mahmud Abbas.