At least nine Afghan soldiers were killed when the rebels ambushed their vehicle in Helmand province on Thursday, said Haji Wali Mohammed, a spokesman for the province's governor.
The Taliban forces sustained heavy casualties in the attack.
"We lost contact with the Afghan soldiers late on Thursday, and their bodies were found today," he said, adding that authorities would hunt down and arrest those who carried out the attack.
The Taliban immediately claimed responsibility for the attack in the district of Chakul.
"Yes, the Taliban did this and we will launch more attacks against government and coalition forces," said Mullah Latif Hakimi, who often speaks for the Taliban.
In neighbouring Kandahar, a US soldier was shot and wounded when he and his unit came under small-arms fire while investigating a roadside bomb on Thursday, the US military said in a statement.
US forces have come up against
stubborn Taliban resistance
A rebel was also injured and taken into custody after the attack. Both men were being treated at a coalition hospital.
The US soldier was listed in stable condition.
Meanwhile, rebels ambushed an Afghan patrol in Khost province, near the border with Pakistan, injuring five soldiers on Thursday. Afghan and US forces fired back, killing six Taliban fighters and injuring another.
Two US helicopters sent to survey the area hours later were attacked from the ground with small-arms fire. One of the helicopters fired back, killing seven more suspected rebels, the US military said.
"Yes, the Taliban did this and we will launch more attacks against government and coalition forces"
Mullah Latif Hakimi,
The injured Afghan forces were taken to a coalition hospital for treatment. Two were released and the others listed in stable condition.
The series of attacks follows a period of relative calm in Afghanistan. Taliban spokesmen have said attacks decreased only because of the harsh winter, and that they would resume once the weather improved. The three attacks on Thursday appeared to make good on that claim.
Taliban rebels have mounted a stubborn resistance across southern and eastern Afghanistan since US forces ousted the Taliban government in late 2001.