People stand on the ruins of the former Somali parliament building in the capital Mogadishu August 1, 2013. [Photo/Agencies]

MOGADISHU - Islamist militants set off several explosions in the Somali capital on Sunday, their spokesman said, demonstrating the rebels' ability to attack the heart of government-controlled areas despite security gains.

The guerilla-style attacks were typical of al Shabaab rebels who have waged a six-year campaign to impose their strict interpretation of Islamic law on the country.    

The militants had fired five mortar shells and hurled several grenades, wounding at least two women, senior police officer Abdiqadir Mohamud said.

Somali security forces responded with volleys of gunfire, witnesses said. Casualty numbers were thought to be low.

"We started a massive military operation across Mogadishu at dusk. It will go on until tomorrow morning," said rebel spokesman Sheikh Abdiasis Abu Musab, promising more attacks over the next few days as the Muslim holy month of Ramadan ends.

Al Shabaab said late last month the rise in coordinated attacks conducted by its fighters pointed to its enduring strength and at the time warned of more attacks in Ramadan.

The African Union peacekeeping force, known as AMISOM, has struggled to control areas won back from al Shabaab. The central government extends little influence beyond the capital where security has improved since peacekeepers flushed the militants out of their bases two years ago.

Uganda's Foreign Minister Sam Kutesa told leaders from troop contributing countries - including Uganda, Burundi, Kenya, Djibouti and Sierra Leone - at a summit in Uganda on Sunday that AMISOM had been stretched to its operational limit. But a summit communique stopped short of calling for extra troops.

"I am afraid the remaining nights of Ramadan will be the worst for Mogadishu," local elder Farah Bulle told Reuters. "They have managed to indoctrinate many fighters to die in the holy month."

The blasts came just as people broke the day's Ramadan fast.

"We heard big crashes while we ate iftar (the evening meal). We ran inside with our plates, taking cover from what sounded like mortar shells," mother-of-three Fatuma Osman told Reuters by telephone from Mogadishu's "Kilometre 5" district.

Residents said the coastal capital, which was a battle zone and much of which still lies in ruins after two decades of conflict, was quiet after the initial flurry of blasts.