Colonel Ayub Kassem said the accident took place on Tuesday.
"The boat sank four kilometres (two and a half miles) off Garabulli (50 kilometres east of Tripoli). We were able to save 52 people of various nationalities. Thirty-six bodies have been recovered so far, 24 of them today (Sunday)," he said.
A pregnant woman was among the dead, he added.
Kassem cited survivors as saying the boat had 130 people on board, including people from Burkina Faso, Cameroon, Gambia, Mali and Senegal.
Kassem was speaking a day after the interim interior minister told reporters that Tripoli could "facilitate" people seeking to reach Europe illegally unless the European Union helps it combat the problem.
"I'm warning the world and Europe in particular -- if they do not assume their responsibilities, Libya could facilitate the transit of this flood" of immigrants towards Europe, Salah Mazek told a news conference.
He said Libya was "suffering" because thousands of mainly sub-Saharan Africans were spreading disease, crime and drugs in the North African nation.
For years, Libya has been a springboard for hundreds of thousands of Africans seeking a better life in Europe.
Many cram into makeshift boats to attempt the perilous Mediterranean crossing to Malta or the Italian island of Lampedusa off Sicily.
Hundreds of people lose their lives each year in shipwrecks.
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