The Minister for Foreign Affairs, Mr Cowen, had "a very fruitful and informative discussion" as part of an inter-governmental conference with the Northern Secretary Mr Paul Murphy in Dublin today.
Mr Cowen said both governments and all the political parties "are working collectively to try and muster a set of circumstances where the necessary political will can be demonstrated which will enable successful elections to be held".
"The important point is too intensify the political dialogue now to have elections," he said.
He described the issue of assembly elections as a "question of political will not a chicken and an egg situation here."
Meanwhile Mr Murphy said both governments were working towards holding the elections in the autumn.
"I think that everybody is aware that we are now in the autumn and we said that we wanted elections to be held in the autumn that we are working for that direction for that aim." Mr Murphy said.
"I believe that that trust and confidence is developing so I want to see an assembly elected in Belfast and I want to see an executive in Belfast as soon as possible. That really is the most important thing that we have to do in the weeks ahead," Mr Murphy continued.
Earlier Mr Cowen, insisted that Northern Ireland Assembly elections must take place to break the political deadlock.
Speaking in Dublin during a round of talks between party leaders, Mr Cowen said this had been the Government's view since the day the institutions were suspended.
Mr Cowen was due to meet Sinn Féin chief negotiator Mr Martin McGuinness and Northern Secretary Mr Paul Murphy in separate meetings in Dublin today. Meanwhile in Belfast Sinn Féin president Mr Gerry Adams was meeting Ulster Unionist Party leader in Belfast.
Mr Cowen said: "We just simply have to have elections.
"That is the Irish Government's position from the first day it was suggested to us they were going to be suspended. It was the day they were suspended.
"We have never agreed with that position. We have constantly argued for their reinstatement, for dates so that people can actually recognise them, that the responsibilities they can take up have every prospect of being adjudicated on by people.
"That is what democracy is about."
Meanwhile, speaking after his meeting in Belfast with Mr David Trimble, Mr Adams said strenuous efforts were being made to resolve the impasse in the peace process.
But he warned there was only a limited window of opportunity to resolve the problems and accused loyalists opposed to the process of restarting violence after a peaceful summer.
Mr Adams described his meeting with the UUP leader as "useful - part of a network of engagement". He said he expected to meet Mr Trimble again.
Speaking at a Stormont news conference, Mr Adams said: "It is very obvious there is a window of opportunity here that is quite limited. I think the onus is very much on the British government to call elections quickly."
He said after two postponements it was quite clear Mr Tony Blair couldn't keep on putting off the poll. He declined to detail his talks with Mr Trimble, saying: "Sometimes the least said the better."
Earlier Mr McGuinness warned that no elections this year could spell the end of the Belfast Agreement.