Embattled Brazilian oil giant Petrobras says the company's CEO Graca Foster and five executive directors have stepped down.

The corruption-wracked firm said in a one-line statement that the board will elect new executive members on Friday.

Petrobras has been mired for months in a corruption case involving several top company officials as well as the heads of many of Brazil's main construction companies. The scandal is widely seen as among the biggest in Brazilian history.

Speculation has been rife that Foster would be sacked, but her friend and ally Brazilian President Dilma Rousseff had been seen as defending her.

Wednesday's brief announcement comes a day after rumors of Foster's departure sent Petrobras shares soaring.