Minister for Foreign Affairs Mr Cowen and Northern Ireland Secretary Dr John Reid are hosting preparatory talks today as efforts intensify to save the peace process.
Amid heightening tensions in the run-up to the Orange Order Parade at Drumcree in Portadown, the parties are steeling themselves for a final push.
Today's meeting with the pro-Agreement parties at Hillsborough, Co Down, is a prelude to make-or-break talks in England to try to end the deadlock over decommissioning, policing and demilitarisation.
The two men met in Dublin yesterday, stressing the urgency of finding a way out of the current crisis.
Dr Reid said it was still possible to find agreement at this late stage: "I believe and I hope we can come to a resolution of these issues - the commitment is there - and recapture the vision of the Good Friday Agreement."
Mr Cowen added: "We have to try and create an atmosphere in which progress can be made. In that respect it is for all the parties to reflect on what they can do to contribute."
Taoiseach Mr Ahern and British Prime Minister Mr Tony Blair will chair the meetings on Monday and Tuesday with the pro-Agreement parties at the Weston Park centre in Shropshire.
It is hoped that by taking the parties away from the media glare and the pressure cooker atmosphere of the marching season, progress can be made to resolve the outstanding issues.
Sinn Fein is expected to come under increased pressure during next week's talks to persuade the IRA to put its weapons beyond use.
PA