DHAKA, Bangladesh — At least 10 Hindu pilgrims were killed and dozens more were injured 12 miles southeast of the Bangladeshi capital, Dhaka, on Friday when an annual bathing ritual turned into a stampede, the police said.

The police said they believed that the stampede, in the town of Langalbandh, was set off by a rumor that a bridge over the Shitalakshya River was collapsing. As the rumor spread, thousands of people crowded onto a narrow pathway that led to one of the riverside platforms used for bathing, crushing three men and seven women underfoot, according to the police superintendent, Khandekar Mahid Uddin.

Every year, Hindus travel great distances — including from Nepal, Bhutan and India — to gather on the banks of the Brahmaputra River and take part in a ritual bath. Mr. Uddin said that the authorities could not determine how large the crowd on Friday was but that it was larger than usual, possibly more than one million people, because the festival fell during a long weekend in Bangladesh.