MOGADISHU (Reuters) - Somalia's al Qaeda-linked militants clashed on Friday with African Union and Somali government troops, who are struggling to extend their control to territory beyond the capital where the Islamist rebels are still able to fire mortar barrages.

The spokesman for the Burundian contingent of AU troops said his unit had been unable to capture the airstrip in Daynile district, al Shabaab's last major stronghold at the edge of Mogadishu.

The AU force (AMISOM) and Somali government troops have to capture Daynile and its airstrip so that they can advance towards the al Shabaab-controlled towns of Afgoi, Elasha and Lafole, a short distance from Mogadishu.

"Mogadishu is in the hands of government and AMISOM, except the Daynile airstrip where al Shabaab is still fighting," said the spokesman, Ndayiragije Come.

He said 20 al Shabaab fighters had been killed in the fighting, while one Burundian soldier had died and four were wounded.

Daynile has been the scene of some of the heaviest fighting in Mogadishu. In October, the AU said it had lost 10 Burundian peacekeepers in fighting there, but Reuters witnesses said they saw a significantly higher number of bodies.

Al Shabaab's military operations spokesman said the rebels had pushed AMISOM and government troops away from the airstrip and had captured a vehicle-mounted anti-aircraft gun. Reuters witnesses said they saw government troops leave the vehicle behind.

Al Shabaab, which wants to impose its harsh interpretation of sharia, Islamic law, has been under pressure since pulling out of the capital in August and losing control of towns in southern and central Somalia to Ethiopian and Kenyan troops.

But its fighters have shown they can still carry out large-scale guerrilla attacks on government targets in Mogadishu using roadside bombs, grenades and hit-and-run raids.

The rebels have fired mortar rounds at the presidential palace over the last two weeks, killing at least seven people in the area around the palace. A suicide bomber blew himself up outside the gate of Villa Somalia, as the presidential palace is known.