CARACAS, Venezuela — Search teams combed the Caribbean on Thursday for 25 Venezuelan migrants missing after a boat sank in rough seas on the way to Trinidad, authorities said.

At least nine others from the sunken boat had been pulled alive from the water, they said.

The small craft left Venezuela on Tuesday and overturned not far from shore, said Lt. Kerron Valere of the Trinidad and Tobago Coast Guard. He said Venezuela was leading the search within that nation’s waters, but the Trinidad and Tobago Coast Guard was assisting.

Lieutenant Valere said the official manifest listed 25 people on the boat, but the authorities had determined that at least 34 were on the vessel.

A 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.