The AU plans to deploy 8,000 troops with a six-month mandate to help forces loyal to the weak interim government take control of the country. The first Ugandan troops began deploying on March 6.
Burundi has offered 1,700 soldiers, but has said it lacks equipment for the mission. Nigeria has offered 850, but has not given details of their deployment schedule.
Malawi and Ghana are also expected to contribute, but the AU is still far from reaching the proposed 8,000.
Karuhanga met Said Djinnit, the AU commissioner for peace and security, earlier in the day. Djinnit was in Mogadishu for a one-day visit during which he held talks with Abdullahi Yusuf Ahmed, the interim president, and Ali Mohamed Gedi, the prime minister.
Djinnit said: "We paid tribute to the Ugandans who have shown great commitment in deploying the first batch of the stabilisation force."
According to AU officials, the next country to deploy will be Nigeria.
Dozens of people have died since January when joint Ethiopian forces went into Somalia to support the interim government to fight the Union of Islamic Courts, which had taken control of much of the country, including the capital.
"A new government in Somalia has raised hopes for democracy, but it is also a uniquely dangerous time"
Mark Latimer, director of Minority Rights Group International
Since the peacekeeping force has been deployed, two soldiers have been injured and flown back to Kampala.
Also on Tuesday, a roadside bomb hit a UN convoy en route to Mogadishu. It was unclear whether the attack was targeting the world body, a UN spokeswoman said.
Three policemen guarding the convoy were wounded but two UN staff were unharmed.
Minority Rights Group International has recently published its Peoples Under Threat list, in which Somalia has overtaken Iraq as the world's most dangerous country for minority groups.
Mark Latimer, director of the rights organisation, said: "There is the spectre of a return of large-scale clan violence - and groups that supported the old order are now under tremendous threat.
"A new government in Somalia has raised hopes for democracy, but it is also a uniquely dangerous time."