"The passengers were taken hostage on Monday morning when they were on their way to the capital Kabul from Takhar province", a spokesperson for the Kunduz governor, Esmatullah Muradi, told Al Jazeera.
The Taliban confirmed that "three buses packed with passengers" were in their custody.
Afghan security forces battled the militants inside the city for five days, as the US carried out airstrikes and send advisers to help ground forces.
This month the Taliban fought an intense battle with Afghan forces to control the strategically important city of Ghazni.
The battle for Ghazni killed at least 100 members of the Afghan security forces and 35 civilians, according to Afghan officials.
Abdul Rahman Aqtash, a police chief in neighbouring Takhar province, said the passengers had been on their way to Kabul.
"So far, there is no news on the fate of the passengers, but tribal elders and local officials are trying to negotiate with the Taliban", Ayubi added.
This comes despite President Ashraf Ghani's call for a ceasefire with the Taliban during the Muslim holiday of Eid al-Adha.
President Ashraf Ghani said it would come into effect on Monday if the Taliban accepted, but the militants have not responded yet.
"The conditional ceasefire will start tomorrow and it will continue as long as the Taliban preserves and respects it", Ghani said in a ceremony celebrating 99 years of independence from British rule.
Taliban sources said their leaders had also provisionally agreed a four-day truce during the annual Islamic feast of sacrifice, though supreme leader Sheikh Haibatullah Akhunzada still had to give his final approval.
The Taliban have resurged in recent years, seizing entire districts across Afghanistan and regularly carrying out large-scale bombings and attacks that have killed scores of people.
"We call on the leadership of the Taliban to welcome the wishes of the Afghan people for a long lasting and real peace, and we urge them to prepare for peace talks based on Islamic values and principles", he said.
"It is our hope, and that of the global community, that the Afghan people may celebrate Eid al-Adha this year in peace, free from fear", he added, referring to the Islamic holiday that starts next week.