So far 49 people are confirmed missing, he said, based on reports from relatives. Bad weather and high waves hampered the search, he said.
It was not immediately clear whether any foreigners were among the passengers.
The wooden ferry had a capacity of 60 passengers but was overloaded and also carrying dozens of motorcycles, said Sri Hardianto, an official at Indonesia's transport ministry.
The 440-square mile Lake Toba, formed out of an ancient super volcano, is a popular sightseeing destination on the island of Sumatra.
Rescue operations had to be halted two hours on Tuesday morning owing to bad weather.
The scenic lake, with an area of about 1,145 square km (450 square miles), has an island in the middle where tourists visit, from which ferries run back and forth. The absence of the ship's passenger manifest causes the valid passenger number data to be determined. "3 motor boats were deployed for evacuation of victims".
A woman cries as she finds out her family is one of missing passengers at Lake Toba ferry port in the province of North Sumatra, after a boat overturned.
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Video footage provided by the agency showed people on another ferry throwing life preservers and life jackets to several people in the water.
According to local authorities, 19 others were rescued, but the rest were still missing.
"I was desperate. I was scared to death. I wish I had died with my family, but I didn't", she told Metro TV in tears.
Rescue workers are battling rain and high winds to try to reach any remaining survivors from Monday's accident.
Maritime accidents are common in Indonesia, a 17,000-island archipelago nation where many depend on ferries and other boats to get around, despite lax safety standards.
It comes after a longboat carrying around 43 people sank off Makassar on Sulawesi island last week, leaving 13 people dead. In the same week, a speedboat carrying 30 passengers sank off South Sumatra, killing two.