The U.N.-backed Transitional Federal Government of President Sheikh Sharif Ahmed controls part of the capital, and AMISOM -- AU troops from Uganda and Burundi -- is fighting to keep two hardline Islamist insurgent groups from taking over the rest.
It has been facing a four-year-old rebellion led by the al Shabaab rebel group which professes loyalty to al Qaeda.
AMISOM said in a statement on Saturday that after a visit to Mogadishu this week by Major General Godefroid Niyombare and General Aronda Nyakairima, the defence chiefs in Burundi and Uganda, the two countries committed more soldiers.
"In a joint statement to field commanders, the chiefs declared that both Burundi and Uganda had committed the additional 4,000 troops mandated by the U.N. in December and that they were already heading for pre-deployment training."
"Each country has pledged a further 2,000 troops and anticipate an efficient deployment around the middle of the year." Burundi has already deployed 1,000 of the 4,000 extra troops in mid March.
The transitional government is seen by the international community as the best hope of returning the Horn of Africa country to stability after two decades of conflict.
AMISOM said it now had over half of Mogadishu under its control.
"We are making steady but consistent progress and we now have 60 percent territorial control as a result of the recently implemented offensive and we will continue to build on this," AMISOM said, adding that integration of government soldiers into its units was also going well.