The Taliban accepted the three-day truce but rejected calls by Ghani to extend it.
The Taliban have been at war with the USA -backed Afghan government for nearly 17 years, and have stepped up attacks in recent years, seizing rural districts and carrying out major assaults against security forces and government compounds on an almost daily basis.
Mohammad Yusouf Ayubi, the head of the provincial council in Kunduz province, said the insurgents stopped the buses near Khan Abad district.
"There were more than 100 passengers on the buses and they were taken to an undisclosed location".
There was no comment from the Taliban but the area of the incident is under Taliban control.
The president's announcement was immediately welcomed in neighboring Pakistan, which has always been accused of fostering links with the Taliban's leadership and providing sanctuary to its fighters.
President Ashraf Ghani declared a provisional three-month ceasefire with the Taliban on Sunday to mark the Eid al Adha holiday, even though fighting against the Western-backed government in Kabul and North Atlantic Treaty Organisation coalition forces has increased.
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Abdul Rahman Aqtash, the police chief in neighbouring Takhar province, said the passengers were from Badakhshan and Takhar provinces and were traveling to the capital, Kabul.
But one of the Taliban commanders said the June ceasefire had only helped USA forces, who the Taliban are trying to drive out of the country, and Taliban leader Sheikh Haibatullah Akhunzada rejected the new offer on the grounds it would only help the US -led mission.
The Taliban has not officially responded to Ghani's offer.
Ghani made the announcement just a day after the leader of the Afghan Taliban said that there will be no peace in the country as long as the "foreign occupation" continues. Zabihullah Mujahid, a spokesman for the insurgent group, said it was still discussing it and would announce its decision soon.
The Taliban have sent delegations to Uzbekistan and Indonesia in recent weeks, raising their diplomatic profile even while carrying out deadly attacks. Muradi said 21 people remained in the hands of the militants.
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".
He said the ceasefire would only be implemented if the Taliban respect it.