Local fishermen and navy search teams rescued 17 survivors and recovered 10 corpses by the end of Friday, Mansaray said.
The remaining 45 passengers were missing and feared dead, he said.
The vessel, named Amunafa, was travelling overnight sday from the capital Freetown to the northern town of Kasirie, when it capsized.
The boat met "hostile weather", Alex Koroma, a station manager for Radio Kolenten, told the AFP news agency by telephone.
Gabi Menezes, Al Jazeera's correspondent in Freetown, said severe weather conditions appeared to contribute to the disaster.
"It is the rainy season in West Afrca and accidents like this are not uncommon during heavy rain storms ... it is not yet clear whether the boat was a ferry or a dugout canoe, which carry over a hundred people," she said.
"If it was a canoe it is not surprising – they are often overloaded and very badly policed."
The boat wass powered by outboard motors and regularly ferried goods and people between Sierra Leone's coastal towns and villages.
"We are still combing the area in search of more bodies but so far, nothing has been found," the police official said.
Kemoh Turay, an official of an association of shipowners said: "There is little hope of finding anyone alive by now."