Afghan forces have begun an operation to retake the city of Kunduz, after suffering a major military reverse when it was seized by the Taliban on Monday.
Security forces have cleared the area around the central prison and the police headquarters, officials said.
The US said it carried out an air strike on the city early on Tuesday.
In one of their biggest assaults since 2001, the Taliban had forced Afghan troops and officials to retreat to the airport and freed hundreds from jail.
The attack on the northern city came as President Ashraf Ghani completed a year in office.
Kunduz is the first provincial capital seized by the Taliban since they lost power in the US-led invasion 14 years ago, and the Taliban’s advance there will pile pressure on Mr Ghani’s unity government.
It said it had deployed hundreds of fresh troops to help with the effort to retake the city on Tuesday.
“Serious fighting is going on,” interior ministry official Matin Safraz told Reuters news agency.
“The Afghan security forces have been retaking most of the strategic parts of the city,” he said.
There were reports from Kunduz that Taliban fighters were trying to melt away among the civilian population.
The Taliban’s new leader, Mullah Akhtar Mansour, said the government should admit defeat.
Kunduz residents “should not be worried about their lives and property” and should “continue as normal”, he said in a statement.
Phone and power services for most of the city were reportedly still down.
A spokesman for the Nato-led coalition in Afghanistan said US forces had conducted an air strike “to eliminate a threat to coalition and Afghan forces” in the area.
Analysis: Dawood Azami, BBC World Service
The seizure of Kunduz has a huge propaganda value for the insurgents. Pictures of Taliban fighters hoisting their trademark white flags in the city’s squares and main buildings have been circulating on social media.
The capture of one of the most strategic and richest cities of Afghanistan will not only cement the credentials of the new Taliban leader, Mullah Akhtar Mansour – it will also embolden the Taliban in general.
The Taliban’s main challenge will now be to hold the city. The way the Taliban behave and govern the city, even if it is for a few days, will demonstrate how far the group has changed since the fall of their regime in 2001.
Meanwhile, they will also try to expand their control in the neighbouring provinces where they already control huge chunks of territory.
Nato ended its combat mission in Afghanistan in December, withdrawing most of its troops apart from a 13,000-strong residual force used for training and counter-terrorism operations.
Kunduz is strategically important as a transport hub for the north of the country.
The insurgent attack began at dawn on Monday as fighters fell upon the city from different directions. They captured key buildings and freed about 500 prisoners, including members of the Taliban, from the jail.
Officials and troops retreated to the airport, though dozens of civilians who fled to the airport were reportedly turned away by security forces.
Medical charity Medecins Sans Frontieres said it was treating more than 100 people wounded in heavy fighting and its facility in the city was full.
Militant violence has increased across Afghanistan since the departure of most US and Nato forces last year.
Kunduz province has seen a number of attacks since April, with the Taliban joining forces with other insurgents.