"We have defeated the enemy and we have pushed them back from all the areas they had captured."
Witnesses and officials from the interim government said opposition groups advanced so close to the presidential palace that African Union (AU) peacekeepers guarding it were drawn into the fight for the first time.
"Amisom [the peacekeeping force] backed us up in this latest operation because the rebels were only one kilometre to the presidential palace," an official said.
"We lost three soldiers in battle and the other side left more dead bodies behind. I do not know their exact number."
The 4,300-strong AU peacekeeping force was visible on the streets on Sunday, but an AU spokesman denied engaging in direct combat.
Major Barigye Bahoku told Al Jazeera that his forces were involved in what he called "a show of force".
"We have not been engaged [in fighting]," he said.
"We moved around in our convoy, with our equipment. We are not supposed to be confined ... rather we are supposed to provide security for all of Mogadishu.
"So we moved in, we showed force and we went back to the base and the government forces are continuing with their work."
Mohamed Sheikh Nor, a journalist in Mogadishu, told Al Jazeera that the fighting was some of the worst in recent days.
"Somali government officials have been requesting the AU peacekeeping force in Somalia, especially in the capital Mogadishu, to be part of the fighting against the opposition fighters.
"But the AU, up until now, has been declining to comment" on why they have not accepted the government's request, he said.
The peacekeepers - from Burundi and Uganda - generally try to avoid being drawn into the conflict in order to preserve their neutrality.
Their mandate includes the defence of the capital's port, airport and key government buildings.
Fighters belonging to al-Shabab and other anti-government groups control large areas of southern and central Somalia and have boxed in government troops and the AU force into a few blocks of Mogadishu.
Sharif Ahmed, Somalia's president, is struggling to take control over the Horn of Africa nation from the fighters bent on overthrowing his Western-backed government.