At least nine others from the sunken boat had been pulled alive from the water, while officials said they were struggling to pin down exactly how many people had gone missing.
The number initially believed to be on the boat increased because officials discovered that several onboard had not been listed as approved crew members or passengers, said Lt. Kerron Valere of the Trinidad and Tobago Coast Guard.
The small craft left Venezuela on Tuesday and overturned in the sea at some point not far from shore, Valere said in a statement.
The Venezuelan government did not immediately make public comments about the accident involving suspected migrants.
Valere said Venezuela was leading the search within that nation's waters but the Trinidad and Tobago Coast Guard was assisting. He said the official manifest listed 25 people on the boat, but authorities had determined that at least 34 were on the vessel.
Venezuelan opposition lawmaker Robert Alcalá said that 25 boarded in the Venezuelan port of Güiria but others illegally got on at another stop along the coast. He said fishermen had rescued several people after the sinking.
Dozens of relatives of the missing were in Güiria anxiously waiting for word back from the search vessels, he said.
Alcalá told The Associated Press that Venezuela's economic crunch of hyperinflation and food shortages drove the passengers - mostly women - onto the boat.
"They go to Trinidad because of the economic situation in this country," he said.
In recent years, an estimated 3.7 million Venezuelans have fled the crisis-wracked country, where a political struggle is now playing out between U.S.-backed opposition leader Juan Guaidó and socialist President Nicolás Maduro.
Most of Venezuela's migrants travel by land into neighboring Colombia and Brazil, but others overload fishing boats to cross the sometimes deadly Caribbean waters to nearby islands.
Migrants often go to border cities and some Caribbean islands to work in the sex industry, allowing them to send money home to families back in Venezuela.
In January 2018, more than two dozen migrants were never found after a boat from Venezuela smashed onto rocks on the nearby Dutch island of Curacao. Officials said two people survived.
The missing boat overturned in strong waves near the island of Patos, a few miles off the Venezuelan coast. Some survivors were found drifting up to 34 miles (55 kilometers) from where the boat sank.
Seven security force vessels were searching for the missing, an official from the civil protection agency said. The official spoke to AP only on condition of anonymity because he was not authorized to speak publicly.
The online news website Daily Express quoted a Venezuelan living in Trinidad who said her sister could not be located. The 21-year-old was headed to the island to flee Venezuela because she said it lacked food and hospital care.
Associated Press writer Soyini Grey in Port of Spain, Trinidad, contributed to this report.
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