By Babak Dehghanpisheh

BAGHDAD (Reuters) - Iraq has begun bombing Islamic State insurgents with help from a new intelligence center with staff from Russia, Iran and Syria, a senior parliamentary figure said on Tuesday about cooperation seen as a threat to U.S. interests in the region.

The center has been operational for about a week, and it provided intelligence for air strikes on a gathering of middle-level Islamic State figures, Hakim al Zamili, the head of parliament's defense and security committee, told Reuters.

The new security apparatus based in Baghdad suggests the United States is losing clout in a strategic oil-producing Middle East, where it has been heavily invested for years.

Two weeks ago Russia started bombing anti-government rebels in neighboring Syria, including the ultra hardline Islamic State, to support its ally, President Bashar al-Assad, to the consternation of the West.

Iraqi officials, frustrated with the pace and depth of the U.S. military campaign against Islamic State, have said they will lean heavily on Washington's former Cold War rival Russia in the battle against the Sunni Muslim jihadists.

Two Russian one-star generals are stationed at the intelligence center in Baghdad, according to an Iraqi official who asked not to be named.

Zamili, a leading Shi'ite Muslim politician, said each of the four member countries has six members in the intelligence sharing and security cooperation cell, which holds meetings in Baghdad's fortified "Green Zone" that once housed the headquarters of the U.S. occupation.

“We find it extremely useful," the Iraqi official said. “The idea is to formalize the relationship with Iran, Russia and Syria. We wanted a full-blown military alliance.”

Iran, a longtime Middle East adversary of the United States, already boasts deep influence in Iraq. Iranian military advisers help direct Baghdad's campaign against Islamic State, which aims to expand its self-proclaimed caliphate in the Middle East.

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It is Russia's participation in the intelligence hub that is causing the most Western anxiety.

Washington, with a history of close security links with Baghdad, now worries the intelligence center may foster closer Russian-Iraqi ties, particularly with respect to operations against Islamist militants, a U.S. security official said.

The United States believes the main point of the intelligence pact, which also covers operations in Syria, is to show that Russia is taking a greater role in the conflict in the neighboring country, said the official.

Prime Minister Haider al-Abadi has said he would welcome Russian air strikes against Islamic State on Iraqi soil.

The Baghdad government, and allied Iranian-backed Shi'ite militias who are leading the fight against Islamic State in Iraq, say the United States lacks the decisiveness and the readiness to supply weapons needed to eliminate militancy in the region. Washington denies such accusations.

U.S.-led air strikes on Islamic State militants who control a third of Iraq, have failed to turn the tide in Iraq's conflict, which has sapped the OPEC oil producer's finances and fueled sectarian bloodletting.

Iraqi warplanes bombed a convoy this week that was thought to be carrying Islamic State leader Abu Bakr al-Baghdadi, based on information from the center, said Zamili. Security officials later said Baghdadi had not been in the convoy.

"We can get a lot of use from Russian intelligence, even if they don't do air strikes," Zamili said.

Sami al-Askari, a former member of the Iraqi parliament and one-time senior adviser to ex-prime minister Nuri al-Maliki, said Iraq was aware of the sensitivities of the new arrangement.

“The Iraqi government wants to do this in a way that doesn’t look like they’re pushing the Americans away,” he said.

(Additional reporting by Mark Hosenball in Washington; Writing by Michael Georgy; Editing by Mark Heinrich)