The Dáil will hold a full debate on the Flood tribunal report next week as the Government moves to reject allegations and political charges arising from the report.
A Government spokeswoman last night rejected claims that Mr Burke had "some information" that put him in a position to demand a cabinet post in 1997. The claims are said to have emanated from sources close to Mr Burke.
Mr Ahern did not directly answer questions about this on Monday, but his spokeswoman yesterday said such claims were "without foundation".
Meanwhile, the Minister for Foreign Affairs yesterday described as "without foundation" other reports that a serving Cabinet member had received an £80,000 payment.
"I know nothing about it. I don't know anyone else that knows anything about it," he said.
Backbenchers continued yesterday to express unhappiness with the Government's response to the Flood tribunal report, which found Mr Burke had received a series of corrupt payments from developers and promoters of Century radio.
However, there was no confirmation last night of a report that a number of backbenchers met in Dublin to discuss the prospect of replacing Mr Ahern as Fianna Fáil leader with Mr Cowen. The report was carried on TV3 News.
Mr Cowen emphatically dismissed speculation he could become party leader in the near future. "There is no leadership vacancy in this party. There is no prospect of a leadership vacancy in this party.
"The Taoiseach has the total undivided support of every sensible person in this party," he told reporters in Dublin.
The Government yesterday agreed to hold a Dáil debate next Wednesday and Thursday arising from the Flood tribunal report.
Fine Gael and Labour had demanded such a debate, with Labour tabling a motion calling for a full statement from the Taoiseach on his appointment of Mr Burke to cabinet in 1997.
The Labour motion also calls on the Government "to outline what steps it proposes to take to undo the commercial damage done to RTÉ as a result of the corrupt action of the then Minister for Communications Ray Burke". Labour has also called for legislation on corporate donations to political parties.
"Five days after the publication of the most damning indictment of any person to hold ministerial office in the history of the State, there is still little evidence to suggest that the Government appreciates the seriousness of the findings of Mr Justice Flood," said party leader Mr Ruairí Quinn.
Fine Gael is to table its own motion today.
The whips from the Dáil parties are to meet in the next few days to discuss the format for the debate, with the Opposition seeking a question and answer format during which they can press the Taoiseach on the events leading up to his appointment of Mr Burke as Minister for Foreign Affairs.
"This debate should be on a substantive motion, along the lines we have suggested, and should not be restricted to a series of statements on the report," Mr Quinn said.
Meanwhile, the Tánaiste, Ms Harney, said last night that Mr Burke "wasn't fit for public office . . . He should not have been appointed".
She said she had asked the Taoiseach to instigate an investigation into Mr Burke in 1997, and it was "a pity" that the inquiries conducted then had not revealed the information that was now available.