Residents say the militants had pushed back into the heart of the city and that there were intense clashes over the governor's office.
The Taliban has denied the city has been retaken.
Kunduz was the first major centre to fall to the Taliban in 14 years.
The city's capture on Monday by the militant group was a huge blow to President Ashraf Ghani, coming on the first anniversary of his taking power.
As heavy fighting continued on Thursday, a doctor at the local hospital told the BBC that they were struggling to cope with the high number of injured people coming in.
A businessman living near Traffic Square in the city centre said that Taliban flag - which had been taken down by government forces earlier in the day - had been raised over the square once again on Thursday afternoon.
He described the situation as "very, very tense" and said the fighting was still going on as darkness fell on Thursday evening.
Kunduz, with a population of around 300,000, is one of Afghanistan's largest cities and strategically important both as a transport hub and a bread-basket for the region.
