He said up to 2,000 of those families had fled to Kabul and other provinces.
Many people took refuge in a school in the city and had been provided with food and other relief items, Kunduz provincial council member Ghulam Rabbani Rabbani said.
Video footage taken by AFP showed dozens of people, many of them women and children, sitting inside tents set up in a school compound.
"We are six families living together here for three days... you can see my children are sitting on the ground," Juma Khan, who fled with his family, told AFP.
"We have still not received any help. A team came today to survey some families but after a few minutes they left," said Akhtar Mohammad, who has also taken refuge in the school.