(Recasts with State and Defense department comments)

By Sue Pleming and Andrew Gray

WASHINGTON, July 27 (Reuters) - U.S. Secretary of State Condoleezza Rice and Defense Secretary Robert Gates travel to the Middle East next week seeking Arab support to stabilize Iraq but they may face an uphill battle from Saudi Arabia.

U.S. officials are increasingly frustrated with Sunni Arab nations such as Saudi Arabia that harbor doubts about Iraq's Shi'ite-led government, seeing it as unable to pacify the country and too close politically to Shi'ite-dominated Iran.

A senior State Department official said on Friday Iraq's Sunni Arab neighbors must send an "affirmative" message of support to the government of Prime Minister Nuri al-Maliki and to Sunni moderates in Iraq.

"We want to see all of the neighbors, particularly such key partners as Saudi Arabia and the (United Arab) Emirates, play in Iraq the kind of supportive and constructive role that will be in their interests as well as ours in the region in confronting the negative forces," said the official, who spoke on condition he was not named.

Rice and Gates will deliver this message when they meet ministers of the six-member Gulf Cooperation Council as well as Jordan and Egypt in the Egyptian resort of Sharm el-Sheikh on Tuesday, followed by meetings in Saudi Arabia.

"The region itself can't sit on the fence waiting. It needs to positively engage as well," said the senior official.

The New York Times reported on Friday that the Saudis had offered financial support to Sunni groups in Iraq and U.S. officials were increasingly concerned about its close Arab ally's "counterproductive" role in Iraq.

The senior State Department official, speaking on a conference call to reporters, sought to play down the Times story and said Rice and Gates were not going out to the region to criticize their allies.

"There may be a perception out here, based on some press stories that I have seen, that we are focused on a chastening message and admonitory message towards some of our partners and allies in the region. That is not the case."

The Times also reported that U.S. military and intelligence officials say nearly half the 60 to 80 foreign fighters who enter Iraq each month are coming from Saudi Arabia and that the Saudis have not done enough to stem the flow.

A senior defense official said the subject of foreign fighters going into Iraq would be discussed during the Cabinet secretaries' visit to the region.

"It's a problem we need help addressing," said the official, who also spoke on condition of anonymity.

Middle East experts said one of the problems in the Saudi-U.S. relationship was that the Saudis felt they had not been consulted enough over U.S. policy in Iraq.

"They are really smarting from the lack of diplomacy with them," said Judith Kipper, director of Middle East programs at the Institute of World Affairs in Washington.

With domestic pressure growing to pull out of Iraq, the Bush administration is scrambling to justify a temporary increase, or "surge," of 30,000 troops into the country before a progress report is due in September.

During their meetings in the region, the pair is expected to provide an assessment of the surge and repeat earlier appeals for more Arab involvement in Iraq.

Rice and Gates have both made several trips to the Middle East this year to call for more help with Iraq, where some 157,000 U.S. troops are battling sectarian violence, Sunni insurgents, Shi'ite militias and al Qaeda militants.

The U.S. ministers will also be canvassing support for a Middle East conference proposed by the White House for this autumn, with the goal of reviving Arab-Israeli peace efforts.

Arab countries have been pushing the Bush administration to pay more attention to the Israeli-Palestinian conflict, saying there needs to be a broader approach to the Middle East rather than a narrow focus on Iraq.

"Efforts to separate Iraq and the Arab-Israeli conflict highlight the link between the two," Jon Alterman of the Center for Strategic and International Studies said.

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