By Sue Pleming

JERUSALEM, Aug 2 (Reuters) - U.S. Secretary of State Condoleezza Rice heads to the West Bank on Thursday to reassure President Mahmoud Abbas of U.S. support and press him to begin serious talks with Israel about a future Palestinian state.

The top U.S. diplomat, who spent Wednesday delivering similar messages to top Israeli officials, closes a four-day trip to the Middle East during which she won tacit Saudi support for a proposed peace conference later this year.

But analysts are pessimistic about Rice's new push, coming at a time when the Palestinian territories are divided between Islamist Hamas, which seized Gaza in June, and Abbas's secular Fatah whose forces dominate the West Bank.

The Bush administration has just 17 months left in office and despite labelling the Israeli-Palestinian conflict a priority, its most pressing concern is Iraq and mounting domestic pressure to bring U.S. troops home.

But Rice has made clear she has faith in Abbas and says he is empowered to negotiate on behalf of all Palestinians.

"We do have in the Palestinian territories a government that is devoted to the international principles, the foundational principles for peace and this is an opportunity that should not be missed," Rice said.

There is concern that, by allying himself so closely with the United States, Abbas will be seen as Washington's puppet. The likelihood of successful negotiations is also dampened by Israeli Prime Minister Ehud Olmert's unpopularity with his own voters.

Olmert told Rice during dinner on Wednesday that Hamas had to be "kept out of the game" as Israel explores new cooperation with the Palestinians.

PALESTINIAN BORDERS

The United States is pushing for both sides to start tackling more prickly issues, such as the possible borders of a Palestinian state.

Abbas would like to negotiate so-called final status -- including the future of Jerusalem, borders of a Palestinian state and the right of return of refugees -- but the Israelis are balking at such a broad commitment at this stage.

One senior Israeli government official said Israel was prepared to begin discussing border issues in general terms with Abbas, but saw the fate of Jerusalem and Palestinian refugees as too sensitive for the time being.

"We're willing to move forward on borders. The government is willing to discuss that," the official said.

The United States is propping up Abbas's security forces as they confront Hamas and Rice is expected to sign a security assistance document on Thursday.

Washington has promised more than $80 million to help train Abbas's security forces and for other uses but the initial handover of funds on Thursday is expected to be little more than $10 million, said a senior State Department official.

During her visit, Rice has also been trying to harvest support for a U.S.-proposed Middle East peace conference, though the date and venue are not known and its mandate is unclear.

A senior U.S. official said it would most likely be held after mid-October because of Ramadan and a string of Jewish holidays throughout September and early October.

Saudi Arabia, which does not have diplomatic relations with Israel and has shunned contacts in recent years, has said it could attend the conference if "substantive" issues are covered there.

A senior State Department official declined to say what conditions Saudi Arabia had attached to attending, but said the initial Saudi response was encouraging.

"They have not said yes, they have not said no," he added.

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