A female suicide bomber blew herself up Wednesday during an address by Somalia's prime minister in Mogadishu, killing four people including the country's Olympic and football bosses.

The young woman detonated her suicide belt as Prime Minister Abdiweli Mohamed Ali was addressing 200 people at the newly reopened national theatre on the first anniversary of the launch of Somalia's satellite TV network.

Somali Olympic Committee president Aden Yabarow Wiish and Somali Football Federation chief Said Mohamed Nur were killed in the blast, which was claimed by Al-Qaeda affiliated Shebab rebels.

The prime minister and seven other ministers standing beside him when the bomber detonated her explosives, were unharmed.

"There are four dead, including the president of the Olympic committee and the president of the football federation," Abdirahman Omar Osman, the Somali prime minister's spokesman, told AFP.

Seconds after the blast, chaos filled the theatre as the dead and the wounded were slumped on chairs or lying on the floor while police escorted some of the injured to awaiting ambulances.

At least seven journalists were also wounded, press freedom watchdog Reporters Without Borders said.

The Shebab, which have been fighting for the past five years to topple the Western-backed government, claimed in a Twitter message that they "managed to lay explosive devices before the ceremony".

"This operation was not carried out by a woman as they (Somali government

officials) claim, but it was meticulously prepared and carried out by a specially trained unit," they said.

Shebab spokesman Sheikh Ali Mohamed Rage had earlier told the pro-Shebab radio Al Andalus the attack was "carried out by people who support the Shebab"

but had stopped short of claiming responsibility.

The Chinese-built theatre was reopened last month for the first time in 20 years at a ceremony attended by President Sharif Sheikh Ahmed and the prime minister.

The president of football's world governing body FIFA, Sepp Blatter, expressed shock at the death of the two Somali sports chiefs.

"I knew both men personally and can only say good things about their endless efforts to promote sport and football in their country. They will be sorely missed," he said.

The slain sports chiefs had last week inspected the reconstruction of the national stadium in Mogadishu, a city which had slowly been coming back to life since Somali and African Union forces secured most of it late last year.

Somalia's deputy sports minister had said people were eager to "benefit from the peaceful atmosphere" in Mogadishu.

The stadium was once used by the Shebab rebels as a training centre, turning the pitch into a firing range to test homemade armour piercing bullets.

But last year, Western-backed AU troops seized the stadium and used it as a forward base for assaults on rebel holdouts before turning it over to the government for restoration as a sports venue.

Despite the lull in street fighting, Mogadishu has been plagued by a series of suicide and grenade attacks since the Shebab abandoned fixed bases in August and reverted to guerrilla tactics.

A suicide bomber last month killed at least five people in an attack at the heavily guarded presidential palace.

In regions under their control, the extremist militia have banned football, watching movies, Western music and dressing, with offenders often flogged or publicly executed.

AU force deputy commander Audace Nduwumunsi described the bombing as a "despicable crime against the Somali people" and UN special envoy Augustine Mahiga also expressed outrage.

"The reopening of the National Theatre is symbolic of the real change that is happening in Somalia: the city is being rebuilt, culture is being revived and hope is being restored," he said in a statement.

Britain, which has sought to lead international efforts to end the crisis, condemned what Prime Minister David Cameron branded a "sickening" and "mindless" attack.

"I utterly condemn the action of these terrorists who have shown complete disregard for the lives of the Somali people and for their desire to bring back normal daily life in Mogadishu.

The United States also strongly condemned what it called an "outrageous attack today in Mogadishu that resulted in a tragic loss of life".

"We offer our condolences to the Somali people, particularly those who lost family and loved ones," White House spokesman Jay Carney said, noting that Somalia had made great recent strides to rebuild after two decades of civil strife.

"We remain committed to the people of Somalia and assisting them in countering Al-Shebab's violence and in returning peace to their country."

Somalia has lacked an effective central government for years, allowing armed groups, pirates and extremists rebels to thrive and establish control in vast regions.