Afghan forces attacked Taliban militant positions in Kunduz on Wednesday in the third day of clashes since the insurgents launched a coordinated attack on northern Afghan city.
Fighting was ongoing at Imam Saheb port, Takhar port and Sehdarak, all outside the city, police spokesman Mahfozullah Akbari said.
Residents were also reporting Taliban fighters in the city centre, a provincial council member said.
"Some Taliban militants were seen around the NDS directorate and in the 2nd and 3rd police district this morning," Zargul Alimi said.
Afghan special forces launched an operation overnight to begin clearing private houses where Taliban militants had holed up, Kunduz governor spokesman Hamdullah Danish said.
"A large number of Taliban militants were killed," Danish added.
A "security ring" consisting of several checkpoints in the city is being implemented to prevent further attacks, Akbari said.
At least two people have died and 71 people have been injured since the fighting started, Kunduz health department head Saad Mukhtar said, adding that most of those injured had bullet wounds. Women and children were among those injured.
The violence came as a conference on Afghanistan got under way in Brussels, where the EU had already pledged economic assistance for the impoverished country's development.
In September 2015, the Taliban took the strategically important city of Kunduz for two weeks, which came as a shock to the Afghan government and to the international community.
It was the first time the insurgents had taken over a major urban centre since the US-led offensive overthrew the Taliban regime 15 years ago.