MEXICO CITY—In 2017, Israeli private investigation company Black Cube secretly recorded senior officials at Mexico’s Petróleos Mexicanos describing widespread bribery and corruption at the state-run oil company.

The audio recordings are part of the evidence in a lawsuit filed last year against the Mexican government by a Mexican oil-field drilling company called Oro Negro. The company claims that Pemex, as the state oil company is known, helped drive Oro Negro into bankruptcy because the driller refused to pay bribes.

The recordings, reviewed by The Wall Street Journal, offer a rare window into endemic corruption at Mexico’s largest state enterprise. Over the course of three months in 2017, Black Cube, at the behest of Oro Negro, secretly made dozens of hours of recordings of former and then-current Pemex officials describing an elaborate pay-to-play system at the state oil company, where bribes were accepted in return for contracts. Oro Negro’s top executives, in turn, face charges in Mexico for allegedly misappropriating funds.

The evidence from the Oro Negro lawsuit forms part of a broad-ranging investigation into corruption at Pemex by the U.S. Department of Justice and the Securities and Exchange Commission, according to people familiar with the matter.

Pemex didn’t respond to requests for comment about Oro Negro’s claims, about the evidence produced in the recordings, or details about other investigations. The state-controlled entity, whose chief executive is appointed by the president and which has three government ministers on its board of directors, frequently refers questions to the president’s office for comment.