The DUP and the UK Unionists have accused the Ulster Unionists of betraying their principles by discussing the internal affairs of Northern Ireland with the Taoiseach.
Both parties refused to meet Mr Ahern yesterday. But both held separate meetings with the North's First and Deputy First Ministers.
During its hour-long meeting with Mr Trimble and Mr Mallon, the DUP repeated its demand that Sinn Fein not be allowed into the executive while the Provisional IRA retained its weapons.
The DUP was represented by its deputy leader, Mr Peter Robinson, and the former MP for Mid-Ulster, the Rev Willie McCrea.
Mr Robinson said the political talks initiated by the First and Deputy First Ministers were "an attempt to simulate activity as a substitute for progress".
He said the issue was not how many departments would be set up but whether Sinn Fein assembly members would be appointed ministers.
It was "reprehensible" that any unionist was meeting Mr Ahern to discuss the formation of the new executive, he said.
"Dublin should have no role in the internal affairs of Northern Ireland and there is no matter more internal than the formation of a Northern Ireland executive. Any unionist who discusses such an issue with the Dublin Prime Minister is betraying any unionist principle he or she ever held."
The UK Unionist meeting with Mr Trimble and Mr Mallon lasted only 15 minutes. The party was represented by its leader, Mr Bob McCartney, and assembly members Mr Cedric Wilson and Mr Paddy Roche.
Mr Wilson said the party had asked Mr Trimble to clarify his position on Sinn Fein's entry into government without decommissioning.
"Mr Trimble refused to state his position. He said it was already well known and he wasn't going to say anything further. We decided to leave the meeting," Mr Wilson said.
The UK Unionists also refused to meet Mr Ahern. Mr Wilson said the make-up of the new executive was a matter for the North's assembly and the Taoiseach should not be involved.
Mr McCartney challenged Mr Ahern to state his position on the appointment of Sinn Fein ministers.