WASHINGTON — The United States hasn’t yet persuaded Saudi Arabia, the Sunni power broker in the Middle East and a close U.S. ally, that it should support Iraq’s Shiite-led government, a senior State Department official said Friday.

It’s an uphill fight.

“We believe the Saudis would best advance their and our interests ... were they to be constructively engaged” in helping the elected Iraqi government succeed, said David Satterfield, Secretary of State Condoleezza Rice’s top adviser for Iraq.

Asked whether the administration has succeeded in that lobbying effort, Satterfield gave a half smile and said, “We continue to make the point to them, for their own sake.”

In an interview with The Associated Press, Satterfield also said the United States is certain that radical Iraqi cleric Muqtada al-Sadr is still living next door in Iran. That contradicts aides to the anti-American religious and political leader.

“We know he’s out of the country, we don’t (merely) think” so, Satterfield said. “He’s in Iran, which is where he has been since mid-January.”

Al-Sadr’s whereabouts are significant because of questions about possible splits among his followers and uncertainty about what his Mahdi Army militia is doing and why.

Al-Sadr’s Shiite militia is widely seen as a main threat to Iraq’s unity and is high on the list of targets for the current Baghdad security operation. The ragtag but highly motivated militia twice fought U.S. forces in 2004, but principally targets minority Sunnis. U.S. military commanders say the militia has mostly chosen to lie low during the security crackdown.

Iraqi Prime Minister Nouri al-Maliki owes some of his political rise to al-Sadr’s support, but Satterfield said the al-Maliki government has followed through on its promise of evenhanded treatment for anyone engaged in violence.

He acknowledged the perception that the Mahdi Army “or political elements of al-Sadr’s movement had a disproportionate pass, if you will, even though they were engaged in negative behavior.”

Al-Maliki’s image is better as a result of evenhandedness, Satterfield said, a selling point U.S. officials have been pressing on the Saudis and others.

Saudi King Abdullah is deeply suspicious of both the motives and abilities of al-Maliki, and has told U.S. officials that he sees little percentage in propping up the Iraqi’s leadership, U.S. officials say. The elderly king, a crucial U.S. ally, has also reportedly said he does not think President Bush’s military crackdown will work.

Vice President Dick Cheney was to lobby Saudi leaders on Saturday during a Mideast tour to boost Arab support for Iraq.

Abdullah refused to see al-Maliki when the Iraqi prime minister made his own tour of Arab countries in April.

And during a regional conference in the Egyptian resort of Sharm el-Sheik this month, Saudi Arabia’s foreign minister was one of the few Arab diplomats al-Maliki did not meet in face-to-face talks.

Saudi Arabia is concerned that the Iraqi government is too close to Iran and is not doing enough to reconcile with Iraq’s Sunni Arab minority, a Saudi official said.

Iran, like Iraq, is heavily Shiite. Saudi Arabia has a predominantly Sunni Muslim population.