A jailed former executive at state-controlled oil giant Petrobras has reportedly implicated dozens of politicians from Brazil's leading political parties in a kickback scheme, a legal development that could shake up next month's general election.

The case centers on alleged kickbacks paid to dozens of politicians by construction firms that were awarded contracts with Petrobras between 2004 and 2012.

Several prominent Brazilian politicians were supposedly implicated by the jailed former director of Petrobras' refining and supply unit, Paulo Roberto Costa, who has reached a plea-bargain deal with the Federal Police.

The politicians he mentioned, news magazine Veja reported Saturday, include the late Eduardo Campos, who was the candidate of the opposition Brazilian Socialist Party when he died in a airplane crash on Aug. 13.

He was replaced by his running mate, prominent former Enviroment Minister Marina Silva, who leads incumbent President Dilma Rousseff in voter-preference surveys.

The list of politicians named by Costa, arrested in March, includes a senior official in Rousseff's Workers Party, or PT, as well as Mines and Energy Minister Edison Lobão, and the presidents of the Senate, Renan Calheiros, and lower house, Henrique Eduardo Alves.

Also named were three current or former governors of states where Petrobras has undertaken large construction projects, including the northeastern state of Pernambuco, where Campos served as governor between 2007 and 2014.

The daily Folha de São Paulo, which did not provide any names, said Costa implicated 49 lower-house lawmakers, 25 senators, as well as the minister and former governors cited by Veja, in the kickback scheme.

All of the politicians cited by the press have denied being involved in the scheme or receiving any type of payment from Costa.

Opposition candidate Aecio Neves, who had been second in the polls prior to Campos's death, said the accusations were the "most serious corruption allegations" in Brazil's recent history and demanded that those involved be prosecuted.

He accused the PT of "robbing" state-run companies to guarantee its permanance in power and indirectly held Rousseff responsible, saying she has controlled Petrobras with an "iron fist" over the past 12 years, as mines and energy minister, chief of staff to former President Luiz Inacio Lula da Silva, and now as head of state.

Neves held off, however, on attacking Silva, who is the favorite to defeat Rousseff in a hypothetical second round of voting on Oct. 26. A runoff will take place if no candidate garners more than 50 percent of the ballots in the Oct. 5 first round of voting.

Despite her ties to Campos, Silva only became a member of the Brazilian Socialist Party last year.

The former environment minister, for her part, defended Campos's integrity, saying the fact that Petrobras invested in the state he once governed does not justify his inclusion on a list of allegedly corrupt officials.

Rousseff, for her part, said the list of politicians is mere speculation because the former Petrobras executive is being questioned in secret.