The vessel, which witnesses say was carrying dozens of passengers, capsized a few kilometres from the Western port town of Mbour shortly after setting off on Sunday.
In a post on X, the navy said that 39 lifeless bodies had been recovered between Sunday and midday Thursday, and that the search was ongoing.
The navy had previously given a death toll of 26.
It is feared the number of dead will continue to rise.
Sunday's sinking is the latest in a string of migration-linked tragedies to occur off the coast of West Africa.
Senegal's coasts are one of the main departure points for thousands of migrants hoping to reach Europe, many heading for the Spanish Canary Islands.
But the Atlantic route is particularly perilous because of the strong currents, and every year officials record thousands of deaths and disappearances from overloaded, often unseaworthy boats.
Senegal's President Bassirou Diomaye Faye described the situation as "unbearable" during a visit to Mbour on Wednesday and vowed to "relentlessly track down" migrant traffickers.
He said that the government was working on policies to tackle youth unemployment, but that the situation could not be "resolved overnight".
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