"Over the next few months, hopefully there will be no more Al-Shabaab in Somalia," Ali told reporters during a visit to Oslo.
"They're collapsing, not only militarily but also they've lost the hearts and the minds of the Somali people," he added.
Al-Shabaab fighters fled Wednesday from their strategic base of Baidoa after truckloads of Ethiopian soldiers and pro-government Somali forces seized the town, the second major loss for the rebels in six months.
Baidoa was one of the Al-Shabaab's main bases and its capture leaves the group's fighters in central Somalia increasingly isolated, with African Union troops also chasing them out of the capital Mogadishu.
The Al-Shabaab have said they withdrew from the town for tactical reasons.
"They're on the run and they're losing ground," Ali said. "We are extending the safety zone and security of the country to every part of the country under control of Al-Shabaab."
He said the rebel-held port of Kismayu would also "soon be in the hands of the TFG (transitional federal government)."
The TFG, which stands accused of corruption and embezzling international aid funds, only controls a small part of Somali territory -- essentially Mogadishu -- and is heavily dependent on the African Union Mission in Somalia (AMISOM).
According to experts, the Al-Shabaab are far from being conquered and could instead be turning to guerilla tactics.
Last week, an international conference in London pledged to help bring an end to the chaos in Somalia, which for the past 20 years has had no central government and has been at the mercy of militias, criminal gangs and Islamic extremists.
Source: Daily Nation