RIO DE JANEIRO—Federal prosecutors in Brazil will file charges Friday against the chief executive of construction giant Odebrecht SA and several other construction-industry executives as part of an investigation into corruption at state-run oil firm Petró leo Brasileiro SA, according to a person familiar with the case.

The expected charges would represent a significant setback for Latin America's biggest construction firm and one of Brazil's most important companies.

Chief Executive Marcelo Odebrecht, along with the chief executive of Brazilian construction conglomerate Andrade Gutierrez and other executives from both firms, were arrested last month under suspicion of money laundering and corruption. The executives have since been held in the southern city of Curitiba, to the strong objections of both firms' lawyers. None of the executives been charged with a crime.

Since their arrests, prosecutors have gathered more evidence of their alleged involvement in the scheme, which will be made public Friday afternoon, the person said. The chief executive of Andrade Gutierrez, Otá vio Azevedo, is also expected to be charged, the person said.

Both Odebrecht and Andrade Gutierrez have denied the allegations made against their executives. Odebrecht has called the arrest of its chief executive unnecessary because it was cooperating with authorities. A spokeswoman for Odebrecht wasn't immediately available to comment Friday. Andrade Gutierrez on Friday again denied involvement with the alleged corruption scheme.

At the time of the arrests, federal prosecutors said that Odebrecht and Andrade Gutierrez "headed the cartel scheme within Petrobras."

Prosecutors allege that several of Brazil's biggest construction companies formed a cartel to drive up prices of Petrobras contracts and kick back some of the money to Brazilian politicians, political parties and executives at the oil firm. Some have admitted wrongdoing in exchange for lesser punishment, prosecutors say, while others have denied involvement and await trial.

The investigation into alleged corruption at Petrobras has expanded outside Brazil since the case was first uncovered last year. The U.S. Securities and Exchange Commission and the Justice Department are both investigating Petrobras, whose shares are traded in New York.

On Wednesday, authorities in Switzerland said they were investigating units of Odebrecht in connection with the allegations, and believe Odebrecht units paid bribes from accounts in Switzerland to separate Swiss bank accounts held by former Petrobras directors. Swiss authorities didn't name specific Odebrecht operating units or the Swiss banks involved.

Petrobras has said it was a victim and is cooperating with authorities.

Write to Luciana Magalhaes at Luciana.Magalhaes@dowjones.com and Will Connors at william.connors@wsj.com

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