Mohammed Adow, Al Jazeera's correspondent in Kenya, said the government's onslaught is believed to have the backing of Ethiopia, which has massed troops on its border with Somalia.
"This perhaps explains why government forces have been retaking the strategic towns from al-Shabab militias without a fight," he said.
Ahlu Sunna wal Jamaa fighters, part of the pro-government forces, chased al-Shabab out of the town of Bulahawa in Gedo, southwestern Somalia, on Monday, without firing a shot.
The towns of Mahaas and Wabho in the centre of the country have also recently been taken by government forces.
Pro-government forces say they want to drive the fighters from the south-central town of Baidoa and strategic southern port of Kismayu.
Until this week the government controlled only small parts of the costal capital Mogadishu.
The US has accused al-Shabab of being al-Qaeda's proxy in Somalia.
Somalia has suffered civil war for the past 18 years and African Union peacekeepers are currently in the country aiming to back Sharif's government.