The US military in Kabul could not confirm the attacks on Tuesday. If confirmed, the losses would be among the largest suffered in a single battle by the Taliban.
In June last year, 40 Taliban and seven Afghan soldiers were reported killed in clashes in the south of Afghanistan, although no US aircraft were involved.
Khan Muhammad, a corps commander in the southern city of Kandahar, said Afghan forces had been engaged in fierce clashes with suspected Taliban near the town of Spin Boldak, which lies on the Pakistani border.
"There has been fighting going on between Afghan forces and the Taliban," he told Reuters. "They called in US support."
He said 20 Taliban had been killed and that fighting continued. A second Kandahar official, who asked not to be named, said at least 28 Taliban had died.
Taliban had harboured al-Qaida
fighters blamed for 11 September
A spokeswoman for the 20,000-strong US-led force in Afghanistan hunting remnants of the Taliban militia ousted by a US invasion in 2001 said she had no comment on the report.
"For security reasons, we can't disclose any details," she said.
Taliban had harboured al-Qaida fighters believed to have been behind the September 2001 attacks on the US. They continue to resist Western forces in the country and the US-backed government.
More than 700 people have died in violence in Afghanistan since August, most of it involving clashes with fighters.