Al-Shabaab has been warring against Somalia since it was ousted from the capital by African Union-led forces in 2011.
He told state run SONNA news agency that, Somalian forces and international partners conducted the two different operations.
"Some 81 militants were killed, a number of vehicles and heavy weapons destroyed." Osman said.
Also Africa Command (AFRICOM) said the midnight air strike on Friday near Mogadishu's Shabel region killed a wide range of al-Shabaab militants.
Al-Shabaab has publicly boasted of its alliance with al-Qaeda and has been warring against Somalia's internationally recognized government for control of the country since it was ousted from the capital by African Union-led forces in 2011.