Somalia's al Shabaab militants said they had stoned an 18-year-old man to death for raping a woman at gunpoint in one of their strongholds in the southern Lower Shabelle region.

The group, which pledges loyalty to al Qaeda, has been losing territory in an offensive by African and Somali troops, but has been determined to demonstrate its authority over areas it still controls.

Al Shabaab said the man raped a 28-year-old woman at gunpoint in the outskirts of her village three days before he was killed on Tuesday.

"This shows we have the power to sentence anyone who breaks Islamic law," Sheikh Mohammed Abu Abdalla, the self-styled al Shabaab governor for the region, told Reuters on Wednesday.

Al Shabaab said the woman would receive a two-year-old heifer - the price of a dowry payment in the area.

In September, Al Shabaab militants said they stoned a woman to death in the southern town of Barawe after a court they had set up declared her guilty of adultery.

The rebels emerged as a fighting force in 2006, waging an armed campaign to impose their strict interpretation of Islamic law.

Somalia has been mired in chaos and conflict since the overthrow of President Siad Barre in 1991