The death toll was expected to rise through the night as rescuers reached rural villages cut off by floodwaters.
The Food and Disaster Management Ministry said Cyclone Aila had killed 100 people in Bangladesh, and a government official in West Bengal state in India put the number of dead at 68, according to The Associated Press.
Storm surges in coastal areas of Bangladesh were particularly deadly, disaster officials said, as nearly half a million people sought refuge in temporary shelters. Fishing boats also were damaged and vast areas of rice paddies and cropland were flooded with salty seawater.
Nijhum Dwip, a low-lying coastal island with 25,000 residents, was reportedly submerged.
"We're quite worried about this island, because reports are coming in that houses and fields have been totally washed away," said Nick Southern, the Bangladesh country director for the aid agency Care. "We are trying to get there today by boat, but the cyclone has made travel almost impossible."
In India, video reports from the city of Calcutta showed snapped power lines, uprooted trees and roofs being torn from houses and commercial buildings. The heavy rains also caused massive mudslides in the Darjeeling tea district, where more than 20 people had died, the A. P. reported.
The cyclone also lashed the Sundarbans, the world's largest mangrove forest and a Unesco World Heritage Site that straddles the India-Bangladesh border. The area is an important home to the Royal Bengal tiger, and the A.P. reported that at least one tiger retreated from the rising waters into a home. Game wardens tranquilized the tiger and planned to release it after the flooding subsided.
The same area was struck in 2007 by Cyclone Sidr. More than 3,500 people died in that storm and 2 million more were displaced.