RAMALLAH, West Bank, July 10 (Reuters) - Palestinian President Mahmoud Abbas said on Saturday he wanted progress in indirect peace talks with Israel before any move to face-to-face talks, which the United States wants the two sides to begin. U.S. President Barack Obama urged the two sides this week to resume direct talks by September. Israeli Prime Minister Benjamin Netanyahu, who met Obama in Washington on Tuesday, says he wants to negotiate directly with Abbas. But Abbas faces heavy domestic criticism over the failure of past negotiations and is wary of agreeing to more direct talks with Netanyahu's right-wing government.

Speaking in Ramallah, Abbas reiterated the Palestinian demand for progress in the indirect proximity talks being mediated by U.S. Middle East peace envoy George Mitchell before any move to direct negotiations.

The indirect talks have been under way for two months.

We said that if there is progress we will go to direct talks. If no progress happens, what is the benefit of negotiations that will be futile and useless, he said.

He was speaking at a religious event to mark the Prophet Mohammad's ascension to heaven.

Abbas said the Palestinians wanted the indirect talks to make progress on two issues: security arrangements and the borders of the state the Palestinians aim to found in the West Bank, the Gaza Strip and East Jerusalem.

Israel occupied the territories in the 1967 Middle East war.

We are still hoping to realise success that will allow us to launch serious negotiations leading to peace, said Abbas, who had a phone conversation with Obama on Friday.

The White House said the leaders reviewed ways to advance to direct talks in the near term.

Abbas said Israel must stop building Jewish settlements on occupied land in the West Bank and East Jerusalem and remove the enclaves under a final peace deal. He did not repeat his previous demand for a complete halt to settlement building as a condition for direct peace talks.

The Palestinians say the settlements, which pepper the West Bank, will make it impossible to establish a viable Palestinian state alongside Israel -- the outcome envisaged by major powers.

Netanyahu signalled on Thursday he would not extend beyond September a 10-month moratorium on new home building in Jewish settlements in the West Bank. He said this week he was prepared to discuss right away the future of Jewish settlements if the Palestinians entered direct peace talks. (Writing by Tom Perry, additional reporting by Ali Sawafta, editing by Tim Pearce)