The Taoiseach's special advisor in 1998 organised talks with the alleged "Real IRA" leader Mr Michael McKevitt three weeks after the Omagh bombing, according to a newspaper report. The Minister for Foreign Affairs Mr Cowen has dismissed the report.
The Labour Party leader Mr Pat Rabbitte and the Fine Gael leader Mr Enda Kenny have both called on Mr Ahern to make a full statement on the matter.
"I am sure it will come as a great shock to the survivors and the relatives of those murdered in Omagh that, within weeks of this terrible atrocity, the Government was engaged in a series of contacts with the 'Real IRA'. They areentitled to an explanation from the Taoiseach," said Mr Rabbitte.
Earlier, Mr Cowen said it was a "ludicrous contention" that the Government offered any concessions to the "Real IRA" in return for a ceasefire.
The report says that Mr Martin Mansergh contacted the group, using Belfast priest Fr Alex Reid as a go-between, to talk about a ceasefire.
According to the Sunday Business Post"Real IRA" sources said that Fr Reid was in telephone contact with Mr Mansergh during discussions with Dundalk republicans in the Redemptorist monastery in Dundalk on September 7th, 1998.
A "Real IRA" army council meeting was held in Balbriggan, Co Dublin the following day and a ceasefire was announced on at midnight on September 9th.
The newspaper says round-the-clock surveillance by the Garda was lifted after the ceasefire announcement.
Last week the Government denied a Channel 4 report that it had brokered a deal with the "Real IRA" in return for a ceasefire after the Omagh bombing, which killed 29 people.