It remained unclear why the boat sank as it headed to the Dutch island, a journey frequently taken by people fleeing Venezuela's economic collapse.
The boat carrying 34 people departed Tuesday night, Venezuela's Regional Civil Protection director Jose Montano said yesterday, adding that two people managed to swim safely to shore in Curacao, which is about 70 kilometres away at its closest point.
He said Venezuelan authorities learned of the incident after relatives of one passenger called for help.
"We also found a lot of wood that's from a boat," he said, adding that debris included gas cans and personal belongings.
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The victims have not been identified, and Huggins said it was unclear whether the two men who made it safely to shore were on the same boat or another. He said they were in police custody.
Curacao's police and coast guard continued their search by land and air, looking for possible survivors or victims, he said.
Venezuelan authorities allege the smuggling of products out of Venezuela to neighbouring countries is one of the causes of the severe shortage of food and other basic products that the South American country has been facing for several years.