(Adds Somali military comment)

By Abdi Sheikh and Feisal Omar

NAIROBI, Sept 6 (Reuters) - The Islamist militant group Al Shabaab took control of a sizeable town in central Somalia on Sunday after African Union forces left the area, the third town the insurgents have seized since Friday, militants and local officials said.

The group, which seeks to overthrow the Western-backed government and impose its strict version of Islamic law, has remained a potent threat in the Horn of Africa country even after being forced out of the capital Mogadishu in 2011.

The African Union peacekeeping force, AMISOM, left Buqda on Saturday night, less than a month after taking control of the town, an economic centre of the Hiran region, from al Shabaab.

"We have taken Buqda town peacefully today. The town is now under our control," said Sheikh Abdiasis Abu Musab, al Shabaab's military spokesman.

Ahmed Nur, a senior Somali military officer, acknowledged that military forces had left the town, but said this was to engage al Shabaab elsewhere, and that it would return.

"AMISOM and our troops have gone to launch operations against al Shabaab strongholds in the region," he said.

Residents said they had been treated brutally by both sides, but some said they welcomed the return of al Shabaab.

"The problem is that the government cannot keep control of the town and it does not want al Shabaab to rule it," said local elder Nur Ibrahim. "Government troops rape, rob and kill us. Al Shabaab also punishes anyone who sells items to the government.

Over the last two days, al Shabaab has taken two small towns in the lower Shabelle region, El Saliindi, 65 km (40 miles) south of Mogadishu on the road to the port of Marka, and Kuntuwarey, on the road from the capital to the port of Barawe.

The al Qaeda-affiliated group regularly attacks the AU-led peacekeeping force and Somali authorities.

On Sept. 1, al Shabaab stormed an AMISOM base in Janale, about 90 km (55 miles) south of Mogadishu, killing at least 12 Ugandan soldiers. Al Shabaab said it had killed 70 people in the assault, which came roughly a year after its leader Ahmed Abdi Godane was killed in a U.S. air strike. (Editing by Edith Honan and Kevin Liffey)