BAGHDAD (Reuters) - A convoy of Shi'ite Muslim militia and Iraqi army forces set out from a base near Ramadi on Saturday toward areas held by Islamic State insurgents, an eyewitness and a local official said.

Pro-government forces are seeking to retake the capital of the sprawling western province of Anbar after the ultra-radical Islamic State overran it last weekend in a significant defeat for the Baghdad government.

The fall of Ramadi is the most serious setback for Iraqi forces in almost a year and has cast doubt on the effectiveness of the U.S. strategy of air strikes to help Baghdad roll back Islamic State, which controls about a third of Iraq.

Anbar provincial council member Azzal Obaid said hundreds of fighters, who arrived at the Habbaniya air base last week after Islamic State took Ramadi, were on Saturday in Khalidiya and approaching Siddiqiya and Madiq, towns in contested areas near Ramadi.

At the same time, Islamic State has been advancing towards Fallujah to try to absorb more territory in Anbar province that would bring them closer to the Iraqi capital Baghdad around 80 km (50 miles) to the east. A pro-government Sunni Muslim tribal leader in the area said on Friday that the jihadist militants were around 5 km (3 miles) from Khalidiya.

Iraqi Prime Minister Haider al-Abadi has sent Shi'ite paramilitary groups to try to retake Ramadi at the risk of inflaming tensions with the region's aggrieved, predominantly Sunni Muslim population.

(Reporting by Baghdad Bureau; Writing by Stephen Kalin; Editing by Mark Heinrich)