According to local sources, two checkpoints were attacked outside the Northern city of Kunduz, Sputnik reported.
Ensuing clashes between Afghan National Army (ANA) soldiers and Taliban militants led to the death of 18 soldiers and 3 police officers. No details of the Taliban's casualties were available.
A further 10 soldiers have been taken hostage by the Taliban, the source added.
Most of the clashes took place along highways between Kunduz and the town of Imam Shaheb, near the border with Kyrgyzstan.
Neither Afghanistan’s Defence Ministry nor Kunduz officials have released any statement on the matter.
The Taliban agreed to observe a one-week reduction in violence before signing the February 29 peace agreement with the United States, which stipulates the eventual withdrawal of all US forces from the country.
After the signing, the Taliban stated that they would resume its anti-government violence, attacking an ANA military base in the Logar province, killing at least two soldiers.
Peace talks between the Afghan government and Taliban are scheduled for March 10, but disagreements over a provision in the US-Taliban deal that stipulates the release of up to 5,000 Taliban prisoners may jeopardize the process.
On Wednesday, the US launched an airstrike against Taliban fighters to defend Afghan forces, an American military spokesman stated, AFP reported.
News of the airstrike in Southern Helmand province --- the first in 11 days --- came hours after US President Donald Trump told reporters he had had a "very good" chat with the Taliban political chief.