RNA - Sheer Ali Kamawal, a local commander of Kunduz police said the attack began at around midnight and fighting was going on inside and around the city, Azertac reported.
Some Taliban fighters had entrenched themselves in homes, the police commander said.
The fighters appear to have slipped through a defensive security line set up around Kunduz, entering the city itself before clashes broke out, witnesses in the city said.
In Kabul, Brigadier General Charles Cleveland, spokesman for Afghanistan's NATO-led force, said he was aware of reports of sporadic fighting in Kunduz but said he had not seen evidence of a major Taliban offensive.
Police spokesman Mahfozullah Akbari said security forces were preparing to drive out the fighters, who had infiltrated the Khak Kani area in the city's Southwest.