Twenty-nine bodies were found on Saturday on beaches around the port of Zliten, while another 14 were discovered on Sunday on a beach near the port of Khoms.
"Residents told us about bodies on the beaches around Zliten," Red Crescent spokesman Mohamed al-Misrati said. "We discovered 25 bodies, then another four."
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Misrati did not give any further details about the nationality of the deceased, but the Tripoli authorities' official news agency reported that they were from Africa.
The Red Crescent expected to recover several more bodies, the news agency cited Misrati as saying.
Later on Sunday another Red Crescent spokesman, Fawzi Abdel Aal, said 14 bodies were on the Siline beach near Khoms, 120 kilometres east of the capital.
The would-be migrants were all from Africa, he told AFP.
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The victims were apparently on a boat that capsized near Zliten, 160 kilometres east of Tripoli.
The North African country, with its 1,770 kilometres of poorly patrolled coastline, is a popular point of departure for migrants seeking to reach Europe.
The most common destination is the Italian island of Lampedusa, barely 300 kilometres away.
More than 600,000 people have reached Europe's shores this year in the continent's worst migration crisis since World War II, according to the International Organisation of Migration.
Of that total more than 3,000 have died or gone missing.
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