An Iraqi special forces policeman carries a RPG in Karamah, south of Mosul Thomson Reuters BAGHDAD (Reuters) - Iraqi special forces backed by U.S. and Iraqi air power took control of two districts of eastern Mosul on Saturday after heavy fighting in which they destroyed nine cars deployed by Islamic State as suicide bombs, the military said.

Infantry and armored division troops also advanced in a nearby neighborhood, destroying three rocket launchers and killing 30 militants, it said in a statement said.

Iraqi troops have been fighting for 10 days inside eastern Mosul, trying to expand their small foothold in the city which Islamic State has controlled since mid-2014, when its leader declared a caliphate in parts of Iraq and neighboring Syria.

The nearly four-week campaign to drive Islamic State out of the biggest city under its control in either country has brought together an alliance of 100,000 Iraqi fighters, also backed by thousands of Western personnel on the ground.

They have faced fierce resistance from a few thousand militants who have deployed hundreds of suicide car bombers and waves of attacks by snipers, assault fighters and rocket teams.

Islamic State has also used a network of tunnels around the city and merged into the civilian population of 1.5 million people still living there, helping it launch surprise raids and ambushes on the troops.

The military statement said the Counter Terrorism Service took control of the districts of al-Qadisiya al-Thania, which it moved into on Friday, and adjacent al-Arbajiya.

Further south, but still on the eastern fringes, troops from the First Infantry and Ninth Armoured divisions attacked the jihadists in the Salam neighborhood.

Security forces and army troops are also advancing on southern and northern fronts close to the city, aiming to open new fronts inside Mosul to put further pressure on the ultra-hardline Islamists.

The attacking forces include Iraqi army troops and special forces and federal police units. Outside the city, Kurdish peshmerga forces are holding territory to the northeast and mainly Shi'ite paramilitary forces are deployed to the west.

They are supported by U.S.-led air power, including jets and Apache helicopters, and Western military advisers who have accompanied Iraqi forces on the edge of Mosul.

The International Organisation for Migration says so far 49,000 people have been displaced by the conflict, the most complex military operation in more than a decade of turmoil since the 2003 U.S. invasion of Iraq toppled Saddam Hussein.

(Reporting by Dominic Evans and Saif Hameed; editing by John Stonestreet)