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.
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 reasserted itself this month with a wave of deadly attacks that have killed hundreds, providing it with additional leverage ahead of nascent peace talks.
President Ashraf Ghani said it would come into effect on Monday if the Taliban accepted. "The United States and our worldwide partners support this initiative by the Afghan people and the Afghan government, and we call on the Taliban to participate", Secretary of State Mike Pompeo said in a statement released Sunday.
The attack occured despite President Ashraf Ghani's call for a cease-fire with the Taliban during the Muslim holiday of Eid al-Adha.
Taliban militants kidnapped dozens of passengers after stopping three buses in northern Afghanistan on Monday, officials said, a day after the government announced a ceasefire with the militants.
The Taliban's resurgence in recent years has seen entire districts of Afghanistan fall under its control.
Calling for the truce on Sunday, Ghani said "the ceasefire should be observed from both sides, and its continuation and duration also depend on the Taliban's stand".
In a statement issued by US Secretary of State Michael Pompei he said: "This plan responds to the clear and continued call of the Afghan people for peace".
The militant leader, Maulvi Haibatullah Akhunzadah, reiterated the group's position that the country's 17-year war could only be brought to an end through direct talks with the US.
Earlier this month, the Taliban launched a major assault on the eastern city of Ghazni, just 120 kilometers from Kabul and the capital of a province with the same name.
Ghani has been trying to nudge the resurgent Taliban, which has been fighting to overthrow the US -backed government in Kabul since 2001, into peace talks.
"We have taken the buses to a safe area to prevent any clashes and we are now identifying members of the security forces", he added, saying civilians would be released.
In a message released on the occasion of Eid al-Adha - and without pointing to any cease-fire - the Taliban leader said on Saturday that the insurgents remain committed to "Islamic goals", the sovereignty of Afghanistan and ending the war.
The battle for the city killed at least 100 security forces and 35 civilians, according to Afghan officials.