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By Caroline Stauffer and Guillermo Parra-Bernal

SAO PAULO, March 22 (Reuters) - Grupo Odebrecht SA , the engineering firm at the heart of Brazil's biggest ever graft probe, on Tuesday agreed to cooperate with prosecutors, in a move likely to send shockwaves across political parties that for years illegally siphoned money from state contracts.

Executives at Salvador, Brazil-based Odebrecht targeted by the probe, known as "Operation Car Wash," will ask for plea bargain deals with prosecutors, a company statement said. It marked a radical shift for Odebrecht, which had previously done little to cooperate in the two-year-old probe. The company said the decision was made to help "build a better Brazil."

The news came as the team of investigators in the probe on Tuesday uncovered systematic corruption at Odebrecht, with an office to pay bribes on work for World Cup soccer stadiums and Olympics legacy projects. Raids carried out at dawn uncovered a parallel bribery scheme that helped extract money from state-controlled oil producer Petróleo Brasileiro SA, or Petrobras.

Several top executives and politicians have already been imprisoned in the case, which could help topple President Dilma Rousseff, who is facing impeachment proceedings for an unrelated matter involving alleged illegal mismanagement of the budget.

Rousseff's political mentor and predecessor, Luiz Inácio Lula da Silva, has been charged with money laundering and fraud. A top senator who also sought a plea deal recently said Rousseff, a former Petrobras chairwoman when much of the alleged graft took place, knew about the scheme.

Both Lula and Rousseff deny any wrongdoing.

"In spite of all the difficulties and the conscience that we are not fully responsible for the facts that Operation Car Wash investigates - which reveal the existence of an illegal and illegitimate political and electoral fundraising system, - we continue to believe in Brazil," the note from Odebrecht said.

The political crisis comes as Brazil grapples with its steepest economic recession in decades and an epidemic of the mosquito-borne Zika virus, just as Rio de Janeiro prepares to host the Olympic Games in August.

Odebrecht is the largest of Brazil's major engineering firms accused of colluding to overcharge Petrobras for work and using the excess as bribes that were funneled to ruling coalition politicians and, in some cases, Rousseff's opponents.

Carlos Fernando dos Santos Lima, one of the case's lead prosecutors, said on Tuesday there is evidence of bribes paid on soccer stadiums built to host the 2014 World Cup, and in particular São Paulo's Arena Corinthians.