“We were really scared,” Mr. Flores said.

As they approached the blue vessel, the crew members onboard ordered the fishermen to raise their hands, communicating through a translator, the fishermen said. They said they were then bound, hooded and held on deck overnight, receiving no medical attention even though some were badly injured, with open, bleeding wounds.

The men, who were armed, questioned the fishermen, asking whether they were carrying anything illegal. When an injured fisherman replied that they had been inspected by the Ecuadorean Coast Guard shortly before the attack, the men began arguing among each other, seemingly worried, the fishermen said.

The next morning, the fishermen said, they were transferred to the Salvadoran Coast Guard and taken to a naval base in La Unión, in El Salvador, where they were treated well. The Salvadoran authorities told them that when they received the Ecuadorean crew, the armed men described their captives only as shipwrecked fishermen. They were then released to the capital, San Salvador, with no charges, the crew members said.

What struck Mr. Flores was his inability to identify the group of men on the blue boat, he said. For decades, he said, he had interacted with the navies and coast guards of Ecuador, the United States and other nations that patrol the waters around Ecuador, one of the world’s biggest routes for the illicit cocaine trade. They often sailed boats that clearly identified what branch of government they belonged to — like the Navy or the Coast Guard — and wore uniforms with insignia to match, the fishermen said.

But these men wore just the American flag patches, and their vessel did not fly a flag or have other markings on it, the fishermen’s lawyer said.