Steven Donziger, a lawyer representing the group of Ecuadorans who are suing Chevron, contending that they had been harmed by the oil contamination, said: “I suspect this is a Chevron sting operation; there needs to be an investigation into Chevron’s role in this as much as the judge’s. I find it awfully odd that these individuals would secretly film meetings using James Bond devices like a spy watch and a spy pen.

Image Flames burning gas in Lago Agrio. A group of area residents is suing Chevron, contending that they have been harmed by oil contamination. The company faces up to $27 billion in damages. Credit... Moises Saman for The New York Times

“At the end of the day this will not affect the underlying case,” Mr. Donziger said, “other than it might cause a short delay if the judge needs to be replaced.”

Chevron said it had obtained the recordings from Diego Borja, an Ecuadoran who once worked as a logistics contractor for the company. The company said Mr. Borja had been working with an American businessman, Wayne Hansen, to secure water treatment contracts. Chevron said that neither man had been paid for the recordings, but that the company paid for Mr. Borja and his family to leave Ecuador because of concern about his safety.

“I’d like to think he brought them to us out of respect for our company and concern for what seemed to be transpiring here,” Charles James, an executive vice president of Chevron, said of the recordings in a telephone interview. “We think this information absolutely disqualifies the judge and nullifies anything that he has ever done in this case.”

In one of the recordings made in June, the political operative, Patricio García, who identified himself as an official in Mr. Correa’s political party, referred to $3 million in bribes to be split equally among the judge, the presidency and the plaintiffs in the lawsuit. Mr. Correa’s party, Mr. García said, would receive the $1 million payment on behalf of the plaintiffs.

In the same meeting, Mr. García told Mr. Borja how to approach Ms. Correa, the president’s sister, about the bribe. “Tell Pierina clearly, ‘Madam Pierina, what we came to do beyond anything else is to participate, participate in the remediation. That’s why I want to make you part of this,’ “ he said.