The Minister for Foreign Affairs and the Northern Secretary have written to the Assembly parties inviting them to state their views on the way ahead following last week's election.
Mr Cowen and Mr Paul Murphy want replies before the end of the month.
The letter, a copy of which is in the possession of The Irish Times, outlines the areas which the governments are willing to discuss under the planned review of the Belfast Agreement next month.
Placed firmly in the context of the Joint Declaration published by Dublin and London last May, the letter makes clear that the review will not re-examine the Belfast Agreement's "fundamentals". Rather it was "a chance for the governments and the parties to reflect together on how the existing arrangements have functioned and to consider their future operation".
Both ministers say the parties have raised issues surrounding the operation of the agreement in preceding discussions. These included questions of designation and the Assembly's voting arrangements. At present, Assembly rules dictate that 40 per cent of designated nationalists and unionists must vote in favour of legislation for it to pass. In the vote for First and Deputy First Ministers, the threshold rises to 50 per cent plus one. Both governments are open to discussion on this question.
The letter also touches on the Pledge of Office with regard to the responsibilities of ministers. This covers the requirement of ministers to uphold their office and the Stormont institutions. It also covers matters relating to the North-South Ministerial Council and the British- Irish Council.
The governments will be particularly interested to receive a reply to their letter from the Democratic Unionists. They are keen to know if the planned review will be seen by the party as the necessary vehicle to get beyond the word "renegotiation" of the agreement.
The Irish Government is understood not to be concerned about the use of the terms "negotiation" or "review", having made it clear that any talks "will focus on the operation of the agreement".
Despite the election results last week which saw the SDLP and the Ulster Unionists overtaken by Sinn Féin and the DUP, the governments insist the Belfast Agreement remains the sole template for political progress.
The Assembly parties were yesterday involved in further discussions as the letter was being sent out.
Mr Murphy met the Ulster Unionists yesterday morning and Mr David Ervine of the Progressive Unionists in the afternoon.
The SDLP held talks with Sinn Féin which also hand-delivered a letter to the Democratic Unionists requesting talks.
Both Mr Mark Durkan and Mr Gerry Adams said afterwards they would work to secure a stronger pro-agreement axis in the review.
"We need a stronger and more determined pro-agreement axis that can work together in the upcoming review to protect the agreement from those who would tear it apart," said Mr Durkan. He said his party would not give in to DUP demands to destroy the accord "or to gouge out key aspects of it".
Mr Adams spoke of the need "to develop and co-ordinate a pro-agreement project between us".
The parties will meet Mr George Bush's special envoy on Ireland, Mr Richard Haass, when he arrives in Belfast today for a series of meetings.