JERUSALEM, May 5 (Reuters) - Israeli Prime Minister Ehud Olmert and Palestinian President Mahmoud Abbas met on Monday to try to accelerate peace talks that have shown little sign of progress ahead of a visit by U.S. President George W. Bush.

The one-on-one meeting, which follows a visit by U.S. Secretary of State Condoleezza Rice, has been overshadowed by a new criminal investigation into Olmert's affairs that has some Israeli commentators questioning his political prospects.

Olmert's office declined to comment ahead of the meeting at the prime minister's Jerusalem residence, where he was questioned on Friday by police over fresh allegations that were barred from publication under a court gag order.

Palestinian negotiator Saeb Erekat said Monday's talks would focus on negotiations on core issues, launched at a U.S.-hosted international conference in Annapolis, Maryland in November, and on an Israeli obligation to halt Jewish settlement expansion.

Rice said she still hoped to seal a statehood deal by the end of this year. Washington wants to see more progress before Bush visits Israel later this month to take part in ceremonies marking its 60th anniversary.

But Israeli-Palestinian talks have been clouded by violence, primarily along the border of the Gaza Strip, and by Israel's expansion of settlements in the West Bank, which Palestinians fear will deny them a viable state.

Rice called Jewish settlements in the West Bank "particularly problematic".

A 2003 peace "road map" calls for Israel to halt construction in the settlements. Israel says it will keep major settlement blocs under any peace deal -- a plan tacitly endorsed by U.S. President George W. Bush in 2004 -- and recently approved new housing projects in the enclaves.

The road map calls on the Palestinians to rein in militants.

Rice on Sunday stepped up pressure on Israel to ease travel restrictions on Palestinians in the occupied West Bank, where Abbas's government holds sway. Hamas Islamists took over Gaza last June.

After Rice's last trip in late March, Israel said it planned to remove 61 barriers in the West Bank. But a U.N. survey subsequently found that only 44 obstacles had been scrapped -- and that most of these were of little or no significance.

Israel says its network of hundreds of barriers in the West Bank prevent suicide bombings. Palestinians view them as collective punishment and a blight on their economy. (Reporting by Adam Entous in Jerusalem and Mohammed Assadi in Ramallah, Editing by Samia Nakhoul)

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