By Ahmed Rasheed and Saif Hameed

BAGHDAD (Reuters) - Iraq may request Russian air strikes against Islamic State on its soil soon and wants Moscow to have a bigger role than the United States in the war against the militant group, the head of parliament's defense and security committee said on Wednesday.

“In the upcoming few days or weeks, I think Iraq will be forced to ask Russia to launch air strikes, and that depends on their success in Syria," Hakim al-Zamili, a leading Shi'ite politician, told Reuters in an interview.

The comments were the clearest signal yet that Baghdad intends to lean on Russia in the war on Islamic State after U.S.-led coalition airstrikes produced limited results.

Russian military action in Iraq would deepen U.S. fears that it is losing more strategic ground in the region as Russia weighs in behind President Bashar al-Assad with airstrikes in Syria and Iran holds deep sway in Iraq.

Iraqi Prime Minister Haider al-Abadi has said he would welcome Russian airstrikes on Islamic State militants in Iraq and powerful Iranian-backed Shi'ite militias hope for a partnership with Russia to counter U.S. influence.

"We are seeking to see Russia have a bigger role in Iraq. ... Yes, definitely a bigger role than the Americans," Zamili said.

Shi'ite militias, long mistrustful of the United States, see Russia's intervention as an opportunity to turn the tables.

Russia's drive for more clout in the Middle East includes a new security and intelligence-sharing agreement with Iran, Iraq and Syria with a command center in Baghdad.

"We believe that this center will develop in the near future to be a joint operation command to lead the war against Daesh in Iraq," said Zamili, using a derogatory Arabic acronym for Islamic State, which is also known as ISIS or ISIL.

Washington has been pressuring Abadi to rein in Shi'ite militias, angering fighters seen as a bulwark against the ultra-hardline Sunni Islamic State, the biggest security threat to oil producer Iraq since the fall of Saddam Hussein since 2003.

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‮"‬The Russian intervention came at the right time and right place and we think it will change all rules of the game not only in Syria but in Iraq also," said Muen al-Kadhimi, an aide to Hadi al-Amiri, the most powerful Shi'ite militia leader.

"The government has been relying heavily on an untrustworthy ally, which is the United States, and this fault should be fixed."

A new dynamic dominated by Russia would put pressure on Abadi, who depends heavily on U.S. support and is at odds with the militias and their Iranian backers.

But with Islamic State showing no signs of weakening, the priority will be finding a formula for stability and the key players are embracing Russia.

"There’s a need to create a new coalition and force that is actually effective on the ground and performs the actual goal of fighting Daesh," said Mohammed Naji, another aide to Amiri.

“There is a serious discussion and inquiry into requesting the Russian air forces to conduct air strikes against Daesh positions in Iraq."

(Writing by Michael Georgy; editing by Philippa Fletcher)