Hopes are growing for a constitution for Europe "sooner rather than later", the Minister for Foreign Affairs, Mr Cowen, said today.
After an hour of talks in Brussels to re-launch the search for a deal he said: "There is a real sense of urgency. The problem won't get any easier with the passage of time."
Today's meeting of EU foreign ministers was the fist since the constitution negotiations collapsed dramatically in December.
Poland and Spain were blamed last month for holding out for too much voting power in a deal designed to streamline EU decision-making to avoid political gridlock after 10 new member states join in May.
Now getting the constitution talks back on track depends on Ireland, holding the EU presidency until the end of June.
Poland is already talking up the chances of a deal, but Mr Cowen was cautious, warning that a "series of complex issues" remain to be settled in addition to national voting strengths.
They include the problem of Prime Minister Tony Blair's "red lines" - keeping the right of national veto over EU decisions on foreign policy, taxation, social security, defence and the euro-budget.
Mr Cowen acknowledged that the work achieved up to the point of break down was "a reflection of progress made".
But he added: "Nothing is agreed until everything is agreed". He went on: "We have had about an hour of useful and good discussions today and there is considerable common ground.
"We are committed to taking the matter forward and concluding it as soon as possible.
"There is a real sense of urgency. The problem won't get any easier with the passage of time."
The Taoiseach, Mr Ahern, is continuing a series of private talks with fellow EU leaders as part of preparations for a full report Ireland will produce at the next Euro-summit in March on the chances of a deal soon.
Mr Cowen added: "We all have a collective responsibility for success. We need if we can to resolve this matter before the euro elections if possible. There is a general appetite for the approach we are taking."
He added: "We can't impose a consensus. We hope our work is generating a positive atmosphere, and there is a growing body of opinion that we need collectively to meet our responsibilities.
If a deal cannot be done by the end of June, the discussions are passed to the Dutch government, which holds the EU presidency for the second half of 2004.