JERUSALEM, July 5 (Reuters/Tom Perry) - The Palestinian prime minister said he pressed demands including a halt to Israeli army incursions in Palestinian West Bank towns in a rare high-level meeting with the Israeli defence minister on Monday.

Prime Minister Salam Fayyad's meeting with Israeli Defence Minister Ehud Barak at a Jerusalem hotel was the first public meeting at such a level since indirect peace talks got underway between the Israelis and Palestinians two months ago.

U.S. President Barack Obama, whose administration is mediating the indirect talks, is due to meet Israeli Prime Minister Benjamin Netanyahu in Washington on Tuesday. Obama wants a move to direct talks peace talks aimed at negotiating the creation of a Palestinian state alongside Israel.

Fayyad, whose supporters include the United States, said he urged Barak to allow Palestinian security forces a wider mandate in the West Bank, occupied by Israel since 1967 and part of the territories where the Palestinians want to found a state.

The Palestinian security forces in the West Bank have been retrained in the last three years with financial and technical support from the United States and the European Union.

Fayyad told Barak the Palestinian forces must be allowed to operate in wider areas of the West Bank, most of which falls under complete Israeli control. Likewise, Israeli forces must halt raids into Palestinian towns and cities.

Quick resolution of both issues is very important in order for there to begin to develop a sense of a state in the making, said Fayyad, briefing journalists on the meeting several hours later from Ramallah, where his government is based.

There was no immediate comment from Barak on the meeting, which was held at the King David Hotel. Barak's office said on Sunday that he would discuss various issues related to relations between Israel and the Palestinians.

Fayyad said he pressed other Palestinian demands including that Israel quickly lift its blockade of the Gaza Strip, governed by the Hamas group which is openly hostile to Fayyad and the Palestinian Authority headed by President Mahmoud Abbas.

Fayyad said Barak had promised the issues he raised, among them Israeli actions in East Jerusalem, would be seriously studied and there will be specific and clear answers to all the issues that were discussed.

The Palestinians aim to establish their capital in East Jerusalem, part of the lands captured by Israel in 1967 along with the West Bank and the Gaza Strip.

The two-decade old Middle East peace process has so far failed to make any progress towards that goal. Reviving peace talks has been a priority for Obama.

Obama's Middle East envoy, George Mitchell, has been mediating between the parties since May with the aim of bringing them to the same table to resolve differences over the creation of a Palestinian state in the West Bank and Gaza Strip.

On Friday, an Obama adviser denied that little progress had been made, saying gaps have been narrowed. Netanyahu wants to move to direct negotiations as soon as possible. Palestinian leaders say the indirect talks have not yet made enough progress to justify face-to-face talks.

They want clear answers from Israel on issues of borders and security -- meaning the frontiers of the future Palestinian state and an end to all military occupation.