Taliban fighters earlier appeared to have breached the city, reportedly raising their flag in a central square.
Fighting is continuing near the city’s police headquarters, governor’s compound and National Directorate of Security headquarters, Reuters news agency reports, citing officials.
Afghan security forces are back in control of the strategic northern city of Kunduz, Nato forces and local police say.
In a major victory, Kunduz was briefly captured by the Taliban in September 2015 but government forces, backed by Nato, recaptured it within days.
Special Forces have been flown in from Kabul to help repel the latest assault.
“The city centre is now in our hands and not in their hands. We are launching an attack to clean up the area,” Kunduz police chief Kassim Jangal Bagh told the AFP news agency.
