The packed Shariatpur 1 vessel, carrying about 200 passengers, capsized in the early hours of Tuesday morning after a collision in the Meghna river, 40 kilometres (25 miles) southeast of the capital Dhaka.
Rescue teams were working to raise the ferry and bring it to shore to complete their search, with about 30 bodies thought to be still trapped inside.
"The death toll is now 66," district police Shahabuddin Khan told AFP after dozens more bodies were found during the morning. "We are trying to float the vessel, which will make the search easier."
Hundreds of distraught relatives gathered at the river's edge for the second day as the dead were laid in lines on the bank for identification.
"Here is my mother, here is mother," a ten-year-old boy cried out and rushed into the water as a diver brought out one burqa-clad woman.
The double-decker ferry plunged 70-feet (20-metres) to the bottom of the river after being hit by the barge at about 2:30 am.
Efforts to salvage the sunken vessel were slow as it was weighed down by hundreds of sacks of chilli it was carrying as cargo.
The exact number of people on board was uncertain as passenger lists are often not maintained properly in Bangladesh and many travellers buy tickets on board.
"We have counted the number of missing this morning after talking to their relatives. We think around 30 people could still be trapped inside," said Samsuddoha Khondker, chairman of the Inland Water Transport Authority.
Khondker said an investigation was under way and that early reports suggested the ship, built in 1991, sank rapidly after it was hit.
Dozens of passengers swam to safety while others were rescued by a passing ferry.
"It's a national tragedy. We are trying to find which oil barge hit the ferry," Shipping Minister Shahjahan Khan said in Dhaka. "We need to have maritime police to improve nighttime navigation on our waterways."
Survivor Rina Begum said that the ferry sunk quickly after a loud noise woke her up.
"Everyone was screaming," she said. "I jumped through a window, but my husband could not. I was rescued by a vessel one and a half hours later. I have 15 relatives missing. We were part of a wedding party."
Boats are the main form of travel in Bangladesh's remote rural areas and accidents are common due to lax safety standards and overloading.
In April last year 32 people were killed after a passenger vessel sank in the Meghna river after colliding with a cargo ship. At least 85 people drowned in 2009 when an overloaded triple-decker ferry capsized off Bhola Island in the country's south.
Naval officials have said more than 95 per cent of Bangladesh's hundreds of thousands of small and medium-sized boats do not meet minimum safety regulations.
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