BAGHDAD (Reuters) - Powerful Iraqi Shi'ite Muslim armed groups on Tuesday pledged to fight any U.S. forces deployed in the country after the United States said it was sending an elite special unit to help combat Islamic State.

Defense Secretary Ash Carter offered few details on the new "expeditionary" group, but said it would be larger than the roughly 50 U.S. special operations troops being sent to Syria to fight the ultra-hardline Sunni militants there.

A U.S. defense official, speaking on condition of anonymity, said the new force will be based in Iraq.

"We will chase and fight any American force deployed in Iraq," said Jafaar Hussaini, a spokesman for one of the Shi'ite armed groups, Kata'ib Hezbollah. "Any such American force will become a primary target for our group. We fought them before and we are ready to resume fighting."

Spokesmen for the Iranian-backed Badr Organisation and Asaib Ahl al-Haq made similar statements to Reuters, expressing their distrust of American forces since the 2003 U.S.-led invasion that toppled Saddam Hussein and the subsequent occupation.

The militias, grouped with volunteer fighters under a government-run umbrella, are seen as a bulwark in Iraq's battle against Islamic State, the biggest security threat to the oil-exporting country since Saddam's fall.

Prime Minister Haider al-Abadi, who came to power more than a year ago with the backing of the United States and Iran, said on Tuesday that Iraq had no need for foreign ground troops and praised the role of his country's special forces and counter-terrorism apparatus in battling Islamic State.

"The Iraqi government stresses that any military operation or the deployment of any foreign forces - special or not - in any place in Iraq cannot happen without its approval and coordination and full respect of Iraqi sovereignty," Abadi said in a statement.

Russia's larger military role in neighboring Syria, and its participation in a security coordination cell in Baghdad that includes Iran and Syria, may be deepening U.S. fears that it is losing more strategic ground to rivals in one of the world's most critical regions.

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On Sunday, two senior U.S. Republican senators called for Washington to nearly triple military force levels in Iraq to 10,000.

About 3,500 U.S. troops are currently advising and assisting Iraqi forces. In October, a U.S. special operations force member was killed during an operation with Kurdish peshmerga fighters to rescue hostages held by Islamic State in the northern town of Hawija.

(Reporting by Ahmed Rasheed; Writing by Stephen Kalin; Editing by Tom Heneghan)