about 100 kilometres south-west of the capital Mogadishu, were struck by two explosions, witnesses said.
A third explosion targeted a convoy of troops rushing to the bases from the capital after the attack, they said.
Hussein Nur, a military officer, said the army lost "several" soldiers in the attack on Bariire and Awdhigle bases.
The army sent in reinforcements from other stations, who killed an unspecified number of attackers in the ensuing fight, he told Reuters.
It was now in control of both bases and the surrounding areas, he said.
"We are pursuing the militants in the surrounding jungle," Mr Nur said.