Northern Alliance troops have halted their advance into Kunduz from the east, fearing hostile fire.
Thousands of Taliban fighters, including the top Taliban commander, have so far surrendered peacefully.
But by dusk, the Alliance had apparently not secured the city, despite expressing hopes that it would be able to do so.
As infantry troops headed toward the city, a dozen tanks halted their advance from the east after only a few hundred yards, fearing hostile fire from surrounding hills as dusk was falling.
Northern Alliance commander General Atta Mohammed has confirmed troops moved into the city from its western edge when they met no resistance.
"Some of our brothers have moved in, but slowly, slowly. We want to do these things peacefully," he said. "Let them surrender, hand over their arms. We don't want fighting."
He says the number of troops surrendering had mounted into the thousands by mid-afternoon. Alliance spokesman Zaher Wasik says top Taliban commander, Noorallah Noori, is in northern alliance hands.
Another top commander, Rashid Dostum, is also at Arganak, the staging point for the surrender and the site where the surrender accord was sealed, Gen Mohammed said.
He added that the former Taliban deputy defence minister, Mullah Faizil, is overseeing surrender operations inside the city.
The Pakistan-based Afghan Islamic Press reports 2,500 Dostum fighters are inside the city and have taken control of its centre, but that could not be independently confirmed.