The boat carrying about 80 people collided with a sand-laden cargo vessel in the darkness late Saturday on the River Surma, local government officials Abul Hashem and Matiur Rahman said.
They spoke to The Associated Press by telephone from the scene of the accident in Sunamganj district, about 110 miles (175 kilometers) northeast of the capital, Dhaka.
Some survivors swam to shore or were rescued by local villagers. The death toll reached 37 after rescuers recovered two more bodies Sunday. Thirty-five bodies were found soon after the accident, the officials said.
On Sunday, rescuers were still searching for about 18 people who have been reported missing, the two officials said.
All the dead were from the passenger boat. Dhaka's Prothom Alo newspaper reported most were women and children.
The boat was traveling from Sunamganj to the neighboring Kishoreganj district.
Boat accidents, blamed on lax rules and unfit vessels, are common in Bangladesh, a delta nation of more than 230 rivers.