On Tuesday, Brazil's Attorney General Rodrigo Janot asked the Supreme Court to authorise an investigation against Ms Rousseff for obstruction of justice.
Mr Janot also accused the former president, Luiz Inacio Lula da Silva, of involvement in the scandal.
Lula has denied any wrongdoing.
The allegations were based on evidence given by Senator Delcidio do Amaral, who as part of a plea bargain agreed to testify against other suspects after being arrested last year.
President Rousseff described Mr Amaral as a compulsive liar.
"The accusations made by Senator Delcidio do Amaral are absolutely irresponsible and above all false," Ms Rousseff told journalists in Brasilia.
"He has lied repeatedly since his arrest. He first accused Supreme Court judges. Than he reneged on those comments and he is now accusing me. I believe the Senator's credibility is rather precarious," she said.
The allegations come as Ms Rousseff is already under immense political pressure.
Senators are expected to vote next week on whether to start an impeachment trial against her over separate allegations.
She is accused of illegally manipulating the federal budget ahead of her re-election in 2014, which she denies.
If the Senate votes in favour of the trial going ahead, Mr Rousseff will be suspended for 180 days.
Mr Janot also asked the Supreme Court to authorise an investigation into Lula for alleged corruption, accusing the former president of playing a key role in the Petrobras scheme.
He said the corruption could not have taken place without the participation of the former leader, who served as Brazilian president between 2003 and 2011.
He requested authorisation to investigate Lula and 29 other senior politicians, officials and businessmen.
Prosecutors say the corruption scheme is estimated to have cost the company more than $2bn (Â£1.45bn).
Part of the money, they say, was used to finance the electoral campaign of top Brazilian politicians.
Several politicians, Petrobras executives and businessmen have been arrested and sentenced as part of the two-year investigation.
Ms Rousseff served as the head of Petrobras for much of the period when the corruption took place, but she has not been implicated in the scandals.
Brazil's President Dilma Rousseff says accusations that she tried to block a major corruption investigation into state-owned oil company Petrobras are "false and irresponsible".