"Most of the victims were buried under the collapsed walls of their homes," he said.
Injured and homeless people have been evacuated to local schools for shelter, authorities said.
PK Dutta, a magistrate in North Dinajpur, told Al Jazeera that casualty tolls are likely to rise.
"Maybe one lakh (100,000) homes have been fully destroyed," he said, adding that tarpaulins, food and other supplies would be given out to those affected.
Across the border in Bagladesh, officials in Rangpur district said two people had died as a result of the storm. A police barracks was also demolished, injuring dozens of people, including two in critical condition.
"The storm has damaged more than 11,000 mud, tin and concrete homes in Rangpur district alone - many of the houses were completely demolished," BM Enamul Haq, a Rangpur district administrator, said.
"It was a huge storm and we are still assessing the damage."