Haitian President Michel Martelly sent a message on Twitter expressing his "sincere condolences to the family and loved ones of the victims" after the 26-foot (7.5-meter) boat packed with 28 people sank after leaving Haiti.
Several children were among the dead, Loretta Mackey, spokeswoman for the Royal Bahamas Police in Freeport, Grand Bahama told AFP, adding that the search for survivors was still continuing.
"At 7:20 pm, the search is still going on, but the number has not changed -- at this time we can confirm 11 bodies, 12 missing and five survivors," she told AFP.
"We don't know when this boat left Haiti, the survivors told us that the capsizing of their boat happened on Sunday, three or four hours off the island of Abaco in the northern Bahamas," she said earlier.
"The migrants were apparently heading to Florida when their engine failed, but we don't have more details," she said. "The survivors were being detained by the police in Bahamas Tuesday for questioning."
A US Coast Guard spokesman earlier said the boat broke up off Hawksbill Cay in the Bahamas on its way to the United States.
Survivors who managed to swim to shore reported the sinking to Bahamian police, who alerted the US Coast Guard on Monday, said Coast Guard Petty Officer Jon-Paul Rios.
Martelly called on his countrymen to "avoid putting themselves in danger by using illegal channels to travel to foreign lands."
He also stressed his "determination to carry on his fight to improve the living conditions for the Haitian people."
Overcrowded boats of migrants regularly try to make it to the coast of Florida from poor countries in the Caribbean like Haiti and Cuba.
Haiti, which suffered a catastrophic 2010 earthquake that flattened the capital and killed more than 200,000 people, is the poorest country in the Americas.