Troops arrive in Mogadishu to aid battle against Islamist insurgents
Al Shabaab, which is linked to al-Qaeda, and another Islamist militia have been fighting Somalia's government since 2007.
Uganda said last month it was willing to send an additional 2,000 peacekeeping troops after more than 70 people died in two blasts while watching the World Cup final in Kampala.
Al Shabaab claimed responsibility for the attacks.
Ugandan soldiers make up the bulk of the 6,100 strong mission known as AMISOM, while soldiers from Burundi protect the presidential palace and guarding the airport.
African leaders meeting in Uganda last month lifted a cap of 8,100 on troop levels in Somalia. IGAD - a bloc of East African Nations - Guinea and Djibouti also pledged to send troops.
A spokesman said the African Union had established the identities of those behind the training and financing of al Shabaab.
"We have 2,000 names," he said, but declined to elaborate.
The insurgents, who control much of the capital and large areas in central and south Somalia, have attracted foreign fighters - including from Britain - to the lawless country.
Eleven militiamen died when their own bombs went off prematurely in Mogadishu at the weekend. They were from Pakistan, India, Afghanistan, Algeria and Somalia.