The anti-government armed militant groups including Taliban militants have not commented regarding the report so far.
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.
Ghani's announcement was also swiftly welcomed in neighbouring Pakistan, which has always been accused of fostering links with the Taliban's leadership and providing sanctuary to its fighters.
The buses, carrying passengers from Badakhshan and Takhar provinces, were on their way to the capital, Kabul, according to Abdul Rahman Aqtash, police chief of the Takhar province.
The Trump administration urged the Taliban to participate in a cease-fire offered by Afghan President Ashraf Ghani, saying it was time to end America's longest war. Some analysts said it might be perceived as an act of desperation by the government following mounting battlefield pressure from insurgents.
A USA delegation led by the country's top South Asia diplomat, Alice Wells, held talks on Afghan peace and confidence-building measures with the group in Doha last month. he insurgents also met recently with senior Uzbekistan officials last week to discuss Afghan peace and energy needs.
Ghani made the announcement while addressing a gathering at Darulaman Palace marking the 99 Independence Day on Sunday.
Provincial Governor Naqibullah Fayeq said on August 19 that the Balcharagh district fell into the hands of Taliban fighters late on August 18 following several days of heavy clashes because the Afghan soldiers did not receive reinforcements.
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.