One of the strikes, carried out on November 9 against IS in northeast Somalia, marked the second time US forces have targeted the terrorist group.
The operation occurred near Bulogudud, about 400 km southwest of the capital city of Mogadishu, the U.S. Africa Command (Africom) said late Sunday.
Unnamed Al Shabaab commander told the group's mouthpiece, Radio Andalus that five American soldiers had been killed after a suicide bomber targeted AMISOM convoy escorting USA officials.
The Somali National Army, working with the Police, Regional Forces and the National Intelligence and Security Agency (NISA), jointly with AMISOM and other partners, will continue to actively seek out al-Shabaab strongholds across the country. "The U.S. forces subsequently conducted the strike under collective self-defense authorities", it added.
Osman's statement came after a series of airstrikes by the USA military in the Horn of Africa nation, which reportedly killed "several" IS and Al-Shabaab militants, in a joint operation with Somali forces.
Washington said Al-Shabaab has pledged allegiance to Al-Qaida and is dedicated to providing safe haven for terrorist attacks across the world.
Somalia on Tuesday vowed to intensify military operations against Islamist State (IS) and Al-Shabaab militants to stabilise the Horn of Africa nation.