The Minister for Justice, Mr McDowell, has criticised the media for a "ridiculous feeding frenzy" in the wake of the revelations surrounding the Flood tribunal report.
The Flood report, published last Thursday, found that former Mr Burke received corrupt payments in the 1970s and 1980s.
"One journalist says something and the rest demand that we respond," Mr McDowell told reporters in Dublin this morning.
The Progressive Democrats minister also asked was it the media's agenda that the PDs should withdraw from the Coalition because Mr Ray Burke lied five years ago. Instead, he said, the Government should concentrate on the "real problems".
Mr McDowell also said if anybody in the media had evidence to back up rumours of a serving Government minister receiving a corrupt payment of £80,000, they should bring it to the Garda or to a tribunal.
Earlier, Labour Party leader Mr Ruairí Quinn accused the Taoiseach of misleading the public over revelations about Mr Burke in the Flood second report.
He said there were still questions Mr Ahern must answer on how much he knew about payments that had been made to Mr Burke when he appointed him as minister for foreign affairs in 1997.
Mr Quinn said the Taoiseach knew before Mr Burke's appointment to the Government that he had received money but still went on to take him on as minister.
On RTÉ radio this morning, he urged the Taoiseach to conduct a debate on the matter, which he described as "murky".
Yesterday, Fine Gael announced details of a private member's motion on the matter. Party leader Mr Enda Kenny said it was a matter of "grave national urgency" that Mr Ahern revealed what he knew about Ray Burke.
