Somalia's embattled government offered an open amnesty on Tuesday to Islamist Shebab fighters after the rebels made a surprise withdrawal from the famine-struck capital over the weekend.

The Al-Qaeda affiliated insurgents had waged a bloody war since 2007 to topple the Western-backed transitional government, which they had hemmed in to a portion of Mogadishu.

"We offer an amnesty -- put down your weapons and your guns, and come and join the people and your society," said Abdirahman Osman, a spokesman for the transitional government.

"For those who have been misled by the senior commanders, now is the time to end the war."

The extremist rebels, who had controlled around half of Mogadishu, abandoned their positions on Saturday, but some units remained active within the capital.

Fighting was reported as rebel remnants clashed with African Union-backed government troops after the pullout.

There was sporadic gunfire reported on Tuesday morning in the city, according to an AFP correspondent.

Government officials celebrated the hardline rebel pullout but the Shebab say it is merely "a change of military tactics."