The incident was reported by Afghan officials in Uruzgan Province on Sunday.
The governor of Uruzgan's Gizab district, Haji Abdullah Khan, said the militants overran the security posts following two weeks of heavy clashes with Afghan soldiers.
The Afghan official said at least 12 militants and four Afghan forces have been killed in the clashes.
He warned that the militants, now heading toward the district center, may gain control over Gizab if local forces do not receive immediate assistance.
Meanwhile, the deputy police chief of Uruzgan Province, Rahimullah Khan, said Afghan security forces had stepped back from some areas in Gizab.
Earlier, a bomb explosion carried out by Taliban militants in Uruzgan’s Deh Rawad district claimed the lives of at least six people, including one woman.
The developments come as the Taliban militants have escalated their attacks against Afghan security forces and the US-led foreign troops across the war-torn country, in their so-called spring offensive.
On June 6, Taliban militants took control over the Yamgan district in the northeastern Badakhshan Province, after launching an offensive there.
Afghanistan has been witnessing violence carried out by Taliban militants since the United States and its allies invaded Afghanistan in 2001 as part of Washington’s so-called war on terror.
The offensive toppled Taliban militants from power, but insecurity still remains across the country.