(Adds further violence, paragraphs 11-14)

MOGADISHU, Dec 6 (Reuters) - The hardline Islamist insurgent group al Shabaab has taken control of a central Somali trading town after fighting that killed at least 13 people and wounded dozens of others, residents said on Saturday.

The capture of Gurael, 370 km (230 miles) north of the capital Mogadishu, adds to the growing hold al Shabaab has gained across south and central Somalia in a two-year insurgency against the government and its Ethiopian military allies.

Locals said al Shabaab, which means youth in Arabic, took Gurael after three days of fighting with a government-allied moderate Sunni Islamist group in the area.

The battle began after al Shabaab fighters arrested a local Koranic teacher of that group, they said.

"I have counted 10 dead men myself," one local resident, Ali Aden, told Reuters by telephone from the area. "Six died yesterday and four were lying in the paths of the deserted town this morning. It is now under control of al Shabaab."

Witnesses spoke of chaos in the area, with bullets being fired on vehicles full of fleeing residents. Three women were killed in one lorry, they said.

More than 5,000 Gurael residents had fled to the protection of nearby woods, a local human rights group said.

Medical staff were overwhelmed.

"We received 15 injured people including civilians and fighters. And we hear many families fled with injuries to other towns," said Ismail Ali, a nurse at Guarel hospital.

Al Shabaab leaders could not be reached for comment.

In further violence, fighting between al Shabaab and local militiamen killed seven people near the southern town of Dobley on Saturday, local residents said. The militant group is strong in that area, near the border with Kenya.

GRENADE ATTACK

In Baidoa, the provincial seat of the Somali parliament, a man threw a hand grenade at government soldiers in a market place on Saturday. The blast killed three civilians and the attacker, witnesses said.

The soldiers shot dead the man who hurled the grenade, witness Hussein Afrah told Reuters.

Since the start of 2007, al Shabaab and other Islamist rebels have waged an Iraq-style insurgency of mortar attacks, roadside bombings and assassinations in Mogadishu, and been gradually taking towns across south-central Somalia.

They hold one town within just a few miles of Mogadishu.

With Ethiopia saying it will withdraw its troops from Somalia by the end of the year, and the Western-backed interim government remaining weak and split, some believe al Shabaab may be poised to take over Mogadishu soon.

It is hampered, however, by splits within the Islamist ranks, where some oppose al Shabaab's militancy and support U.N.-brokered peace talks aimed at a power-sharing government. (Reporting by Abdi Sheikh and Abdi Guled; Mohamed Ahmed in Baidoa; Writing by Andrew Cawthorne; Editing by Charles Dick)

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