The cyclone destroyed thousands of homes and stranded millions of people in flooded villages before it began to ease Tuesday. The death toll will likely rise in both countries as rescue workers reach cut-off areas.
Mudslides in India's famed Darjeeling tea district killed at least 22 people overnight, said Asim Dasgupta, the finance minister of the worst-affected West Bengal state in India.
The official death toll in India stood at 78 by Wednesday, Dasgupta told reporters, adding about 2.3 million people were affected or stranded in flooded villages.
Bangladesh's Food and Disaster Management Ministry said the toll there was 113 after more bodies were found. Most victims drowned or were washed away when storm surges hit coastal areas.
Soldiers have been deployed to take food, water and medicine to hundreds of thousands of people stranded in flooded villages, Bangladeshi Minister Abdur Razzak told reporters Wednesday. In India rescuers evacuated more than 41,000 people by Wednesday, Dasgupta said.
At least 500,000 villagers were affected or stranded, mostly by flash floods caused by tidal surges, said Ziaul Alam, the local administrator in Bangladesh's Khulna district.
The cyclone also caused damage in the Sundarbans, a tangle of mangrove forests that is home to one of the world's largest tiger populations.
Conservationists expressed concern over the tigers' fate.
At least one tiger from the flooded reserve took refuge in a house. Forest guards tranquilized it and were planning to release it once the waters subside, said Belinda Wright of the Wildlife Protection Society of India, which assisted in the operation.
It is believed about 250 tigers live on the Indian side of the Sundarbans and another 250 live on the Bangladeshi side.
Conservationists in India said water levels were too high for ecologists and forest officials to enter the area and assess the extent of the damage.
N.C. Bahuguna, a senior Indian conservation official, said water sources were likely contaminated by salt water from the sea.
Abani Bhushan Thakur, a local forest department official in Bangladesh, said there were no reports of damage or casualties in their part of the Sundarbans mangrove forests.