Mogadishu - A Somali rebel group has told the Horn of Africa nation's embattled leader to quit power and said hardline Islamists had succeeded where government had failed, establishing order in areas they controlled.

Hisbul Islam, which has waged a three-year insurgency against the fragile interim government alongside the al Qaeda-linked al Shabaab group, urged Somalia's Muslims to unite and join in the holy war.

Hardline Islamist control much of the capital Mogadishu, hemming the government into just a few blocks manned by African Union (AU) peacekeepers, as well as vast tracts of south and central Somali.

In recent days, the militants have intensified their offensive on government targets and killed four Ugandan peacekeepers deployed near the presidential palace.

Bent on imposing a strict version of Sharia law on the nation, the militants routinely mete out stonings and amputations and have banned football, music and school bells in areas they control. They claim to have restored law and order.