Among those wounded in the suicide blast was the police chief of Kunduz province, Manzor Stanekzai, Efe news reported.
The incident occurred at around 6 pm when Stanekzai was talking to a group of reporters in the central part of Kunduz city about the security situation, Interior Ministry spokeswoman Marwa Amini told EFE.
"Ten people died and five others were wounded in the explosion," she said, without identifying the victims.
An official from the Kunduz governor's office told EFE that Stanekzai had been wounded and was receiving medical attention.
"The health status of the Kunduz chief of police is stable and he is out of danger," the official, who spoke on condition of anonymity, said.
The Taliban claimed responsibility for the suicide bombing, which occurred as pro-government forces and the Taliban were fighting on Kunduz's outskirts for control of that provincial capital.
They also said the casualty count was significantly higher.
"A big attack was carried out against the chief of police and the commandos of Kunduz in the centre of the city. According to the initial information on this attack, dozens of police and soldiers died or were wounded, including the chief of police of Kunduz," Taliban spokesman Zabihullah Mujahid said in a statement.
The Taliban attacked Kunduz in the wee hours of Saturday, entering the city from different directions and taking control of several of its checkpoints and neighbourhoods.
Authorities said at least 56 insurgents died and an unknown number of soldiers were killed in the clashes.
The attacks coincided with the ninth round of negotiations between a US delegation and Taliban representatives in Doha, where they are trying to hammer out an agreement that brings an end to the 18-year Afghanistan war.
The sides are working on a deal that would see US forces gradually withdraw from Afghanistan in exchange for a pledge from the Taliban not to allow the country to become a haven for international militants.
( With inputs from IANS )