Catching such culprits involves immense challenges.

To start with, the rivers of the Amazon Basin course through a region almost the size of the contiguous United States. Ships on the main waterways can go days without seeing the police or navy boats. Pirates often know the rivers and surrounding terrain better than security forces, and can drop out of sight into far-flung villages.

Police officers here in Amapá State also complain that pirates often carry out their attacks in one state, only to dart over the border into a neighboring one with a different jurisdiction.

“Catching pirates is like waging war against guerrilla fighters,” said Capt. Lúcio Lima, the chief of a special operations unit of the Amapá police force that hunts down river bandits. “They are elusive foes who make the most of their knowledge of river currents, geography and topography.”

When two Polish explorers — Dawid Andres, 41, and Hubert Kisinski, 33 — traveled the length of the Amazon River this year on pontoons outfitted with mountain bikes, they faced challenges from piranha-infested waters to whirlpools.

Still, they said their scariest moments came when pirates in Brazil approached them on three occasions. Each time, they said, they were able to talk their way out of daunting situations.

“It’s the stuff of a nightmare when a crew in Ray-Bans holding huge guns approaches you on the river,” Mr. Kisinski said. Recalling one episode, he said that he and Mr. Andres had calmly explained that they were traveling without valuable items, and then asked the pirates if they had any beer to relieve the stress of the situation.

“That calmed them down a bit; they even started to laugh,” Mr. Kisinski said. “One needs to keep a clear head when facing pirates in the Amazon.”