The MV Maharaj capsized overnight after an accident in the Buriganga river on the outskirts of Dhaka.
Thousands of relatives, many distraught, have gathered at the accident site to watch the salvage operation - fearful that many more bodies may be discovered in the ship's hull.
Authorities estimate that at least 120 people are missing from a ferry carrying over 200 people, according to survivors, although earlier reports said the official number of passengers was only 167.
The ferry was sailing to the southern town of Chandpur from Dhaka when it got caught in a sudden tropical storm on the Buriganga river late on Saturday.
"We have found 74 bodies, and search for more bodies is continuing," Saiful Haque Khan, a director of Bangladesh Inland Water Transport Authority supervising the rescue operation, said.
Police used batons to disperse hundreds of grief-stricken relatives who thronged the Buriganga banks and became angry at the slow pace of the rescue.
"I am waiting to know the fate of my missing mother, sister and five other relatives. But no one is able to tell me anything," survivor Shahidul Islam said.
Many bodies could be trapped
inside the sunken vessel
"Why they are taking so long to bring the ferry out of water? How long shall I have to wait?"
Rescuers said they believed many bodies could be trapped inside the sunken vessel, which they expected to be salvaged by late Sunday afternoon.
Survivors said the ferry, packed with people heading home for a holiday to mark the Muslim religious occasion of Ashura, was on a scheduled voyage when it sank.
"We felt our ferry hit by another vessel in dark. The ferry then listed on one side and began sinking," one survivor told reporters, as rescuers piled up bodies on the river bank.
"I jumped into the water and swam to the shore," survivor Muhammad Jasim said. Officials said they were investigating the report.
At least 200 people died when two ferries sank in the river Meghna near Chandpur in a sudden storm last year. Maritime officials often blame the accidents on unfit and old ferries that sail on Bangladesh rivers.