The identities of the captives have not been made public, but Mohammad Yusouf Ayubi, the head of the provincial council, said the insurgents likely targeted the three buses to try to abduct civil servants or members of the security forces.
He said his forces had not kidnapped the passengers but had taken them to a safe place near the highway to question them and will free them after the investigations are finished.
"Our leadership feels that they'll prolong their stay in Afghanistan if we announced a ceasefire now", a senior Taliban commander, who declined to be identified, said by telephone.
The president, however, linked the ceasefire with similar announcement from the Taliban side and added sustainability of the truce belonged to the Taliban commitment.
Esmatullah Muradi, a spokesman for the governor of Kunduz province, said the kidnapping happened when three buses were travelling through Kunduz from Takhar province, on their way to the capital, Kabul.
Morata reveals why he didn't leave Chelsea this summer
The 2-2 (at half-time) is soft for us because we had more chances to score". I remember better good things instead of the worst. We have to improve which I think is normal.
The United States on Sunday welcomed the announcement by Kabul of a provisional ceasefire with the Taliban, saying the plan "responds to the clear and continued call of the Afghan people".
The incident came a day after USA -backed President Ashraf Ghani called for a temporary cease-fire with the Taliban to coincide with the holiday.
Mujahid said top leaders had not declared a ceasefire, but they would release at least 500 prisoners, including members of the Afghan security forces on Monday, a day before Eid celebrations begin. Some analysts said it might be perceived as an act of desperation by the government following mounting battlefield pressure from insurgents.
There has been a resurgence of the Taliban in recent years, with the insurgents seizing entire districts across Afghanistan and regularly carrying out large-scale bombings and attacks that have killed scores of people.
U.S. Secretary of State Mike Pompeo said in a statement that an earlier three-day cease-fire in June coinciding with the Eid al-Fitr holiday revealed the "deep desire" of the Afghan people to end the conflict, "and we hope another cease-fire will move the country closer to sustainable security". However, the Taliban said it had chosen to release the vast majority of the hostages.