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.

He greeted an 80,000-strong crowd at Newcastle Civic Centre with the words "Haway the lads" to deafening cheers.
President Carter wanted to recruit people for an exchange programme between the north-east of England and his home in Atlanta, Georgia.
His visit on 6 May 1977 is being remembered and celebrated with film footage and talks at the civic centre.
Mr Carter's wife Rosalynn had set up the  Friendship Force to give people in different countries the chance to stay in each others' homes.
In July 1977, hundreds of people from the region jetted off to Atlanta, among them former BBC Look North television presenter Mike Neville.
He said: "Few of us had been to America before - also we were on a jumbo jet and one had never landed at Newcastle Airport before, which was a thrill in itself.
"It was a buzz, I don't think anybody slept the night before. It was just a total, utter thrill.
"The reaction when he got off the plane in America was unbelievable, the crowd cheered and screamed."
Democrat Mr Carter became the 39th president when he was elected in 1976.
He chose to visit Tyneside just a few months in to his term. He left office in 1981.

Columnist and government critic Farhad Mazhar sparked a police hunt after leaving his Dhaka home on Monday morning.
There were reports of a ransom demand.
Police said Mr Mazhar, 69, was eventually found on a bus travelling to the capital from the south-western city of Khulna. It is unclear if he had been abducted.
Human rights groups say enforced disappearances and abductions are rising in Bangladesh.
Mr Mazhar is a supporter of the opposition Bangladesh Nationalist Party (BNP).
Party officials say many of their activists and supporters have been detained illegally since 2014.
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".
[NEXT_CONCEPT]
It is 40 years since US President Jimmy Carter visited Tyneside on his first foreign trip.
[NEXT_CONCEPT]
A well-known Bangladeshi human rights activist has been found on a bus after his family reported him missing.