By Wafa Amr

RAMALLAH, West Bank, May 24 (Reuters) - Palestinian President Mahmoud Abbas said on Saturday he feared a criminal investigation of Israeli Prime Minister Ehud Olmert and looming U.S. elections could hold up Middle East peace talks.

Senior Abbas aide Tayeb Abdel-Rahim reported the Palestinian president's briefing comments to his ruling Fatah faction in the West Bank city of Ramallah on the latest developments in U.S.-brokered peace talks with Israel.

Abdel-Rahim said Abbas "hopes that recent events, such as the obstacles facing the Israeli prime minister, and American preoccupation with elections would not obstruct the peace process desired by Palestinians".

Israeli police questioned Olmert on Friday for a second time. Israel's chief prosecutor said on Monday investigators suspected Olmert had taken cash-filled envelopes from New York fundraiser Morris Talansky.

Olmert, who was first questioned three weeks ago, has denied any wrongdoing but said he would resign if indicted.

On Thursday, Abbas said negotiatons with Israel on sensitive final status issues were continuing, but that gaps were still wide between the sides.

The issues include the fate of Jerusalem, Jewish settlements, setting borders and the right of return for refugees.

Western diplomats and Palestinian officials said Abbas had told them he believed Olmert was serious about reaching a final deal with the Palestinians despite his problems at home.

Olmert and other Israeli officials have reported some progress in the U.S.-sponsored talks but chief Palestinian negotiator Ahmed Qurie said no agreement had been reached yet on any of the issues under negotiation.

The Palestinians are also worried that the Americans' preoccupation with presidential elections, scheduled for November, will push peace moves away from the spotlight.

"It will take the new administration time to settle in before it turns its attention to our problems," a Palestinian official said.

Israeli and U.S. officials have said even if a deal is reached this year, it will not be implemented as long as the Islamist Hamas group continues to control the Gaza Strip.

Hamas, which refuses to recognise Israel, seized the Gaza Strip from Abbas' Fatah security forces in a brief and bloody civil war last June.

Abdel-Rahim said Abbas told Fatah officials on Wednesday that "internal Palestinian divisions, and Hamas' coup ... have weakened the Palestinian (negotiating) position". (Editing by Ori Lewis and Andrew Roche)

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