Rescuers found one survivor, suffering from severe dehydration, on Wednesday on the West Caicos island.
Most of the survivors were found sitting on reefs close to the main islands.
"Of the estimated 200 Haitians aboard the vessel, 118 were safely transported to shore and 15 were recovered deceased," the coast guard said in a statement.
Based on statements from survivors, the overloaded, rickety vessel left Haiti with about 160 people aboard and then stopped along the way, picking up more people.
The boat capsized and sank about 4km southeast of West Caicos. Police were only alerted to the disaster after five migrants were picked up by security staff on the island on Monday afternoon.
Haitians often leave their country in crowded boats in an attempt to escape poverty and find work in the Bahamas or Florida.
"Ill-advised voyages on grossly overloaded vessels are inherently dangerous and should not be attempted," Branham said.
"There are safe and legal ways to immigrate to the United States. When people deviate from these means, tragedies occur."
Last week, coast guards intercepted 124 Haitian migrants from what they called a "grossly overloaded" vessel about 240km southwest of the site of Monday's wreck.
"[The accident] gives you an idea of the stakes that these migrants are willing to face in order to come to a place of greater economic prosperity," Al Jazeera's Nick Spicer, reporting from Providenciales, the capital of the Turks and Caicos, said.
"Haiti is the poorest country in the Americas and it has been pounded by hurricanes and bad weather of late.
"All of the efforts by the international community to improve the lot of Haitians have been hurt by the weather but also by the typical inertia that you find in the United Nations and the aid agencies," Spicer said.
"That is why Haitians hop on rickety boats to go across 1,200 kilometres of ocean to the US in an attempt to improve their lives - because the aid to Haiti is not arriving fast enough."