AU envoy Mahamat Saleh Annadif praised the latest push against the Islamist fighters.
“We will employ all the means at our disposal to end their reign of terror,” Annadif said.
Recent Shabaab attacks in Somalia have targeted key areas of government, or the security forces, in an apparent bid to discredit claims by the authorities and AU troops that they are winning the war.
Foreign diplomats say the Shabaab threaten several nations in East Africa, including Djibouti, Ethiopia, Kenya and Uganda, who all have troops in Somalia.