Minister for Sport Patrick O'Donovan said he wants to see "realistic" and "achievable" deadlines in place for the amalgamation of the GAA, LGFA and Camogie Association.
Earlier today, GAA president Jarlath Burns admitted that the stalling of integration is due to financial concerns at the top level of Gaelic games in equally funding male and female teams.
Dr Mary McAleese, the former President of Ireland, yesterday stood down as chairperson of the Integration Committee overseeing the amalgamation of the GAA, LGFA and Camogie Association.
McAleese cited changes to agreed timelines, a GAA management committee that she described as "less than impressive", and her feeling that there were "people who are not entirely happy about the idea of including women in decision-making at the top level of Gaelic sports" who were holding the process back.
"It is far better to get this right than to rush it," he said.
Ryan has written to GAA clubs across the country to reaffirm the organisation's "commitment to deliver integration for the wider Gaelic games family".
In the letter Ryan said he wanted to acknowledge the "sterling work of Dr McAleese and her significant contribution to the process so far".
Ryan told GAA members that while significant progress had been made on one membership and various other aspects of what is a "complex project", there is still ground to be covered on the structural make-up of the new merged organisation.
He said it was "our belief that it was unreasonable to ask people to sign up to membership of an organisation that wasn't clearly configured", adding that in the absence of required clarity, it was not prudent to proceed with the Special Congresses at this time.
"This is definitely not a pause, a deferral or a suspension of the project," he wrote. "Our work continues as we progress towards publishing a revised and phased plan to achieve integration. We embark upon that work in full collaboration with our colleagues in the LGFA and the Camogie Association."
Burns met with Minister O'Donovan this afternoon, while Dr Mary McAleese and representatives of the Camogie Association and LGFA also held meetings with the Government representatives.
Speaking after this afternoon's meetings, Minister O'Donovan said the Government are "considerable financiers" to all three organisations.
"We want to be part of the solution in terms of the financial requirements that will be needed into the future as well," he said.
Mr O'Donovan said while recent developments were a "massive setback", he asked all three organisations if they were committed to integration.
"All three have confirmed that," he added.
"There has been nothing said to me that would dissuade me from understanding or accepting that integration is ultimately the objective of all three organisations.
"All three assured me they are in when it comes to integration."
Minister O'Donovan confirmed the steering group will meet again on 8 October and report back to the Government, and said he hopes a new chairperson will be appointed by then.
On RTÉ's News at One, Burns described Dr McAleese's comments as "very regrettable".
He revealed uncertainty over how they can fund the top level teams in the inter-county system to the same degree is at the heart of their concerns.
He also defended the GAA’s management committee, which has nine female members out of 19.
Burns said: "I just hope that in the fullness of time, Dr McAleese will reflect on that part of her remarks yesterday and maybe clarify them because it is quite offensive to the people who are on that committee.
"Every national committee has significant female representation. And in fact, five of our national committees are chaired by women
"The GAA Management Committee that I chair is one of the most wonderfully dynamic, intelligent committees that we have in the GAA."
The GAA have said they wanted to put more focus on equity than equality, something which the president explained in greater detail this afternoon.
He said there are uncertainties over spending money preparing male and female teams at inter-county level.
Burns explained: "I want every single girl who plays the game to feel the same way as every boy playing. And I think that there was a lot talked yesterday about the word equity and equality. I feel that equity is a staging post on the road to equality.
"The GAA has committed significant infrastructure resources to ensuring that that happens with all of the hubs that are being built all around the country and virtually maybe in a third of the counties.
"It's the high-performance county level [where the biggest issue lies]. And you have to remember that GAA county secretaries reside in the world of logistics and GAA treasurers reside in the world of invoices. And we have to be respectful of those volunteers.
"So if you look at the main areas of high-performance, development squads, gear, nutrition and catering, gym membership, size of panels, number of sessions per week, travel and expenses, transport of teams, team holidays and training weekends, we already operate an equitable model within the GAA where maybe in a county where football might be the developing code, the hurlers get maybe more resources presented to them. And it's the same with the opposite.
"We actually have a poor record in the GAA of controlling expenditure currently.
"If we go straight into equality, the €45m which we currently spend preparing county teams goes to €90m. We just simply cannot sustain that.
"It’s about resources and the allocation of resources and fundraising that our county volunteers have to do.
"I have to remember that I'm the president of the GAA and I'm accountable to the membership of the GAA. And in every county I go into, I hear the same thing from county treasurers and county chairs that say 'we have to be very careful that we don't just double our expenses on county teams'.
"That is why I have set up a certification committee to ensure that we try and regulate county expenses in the interest of whenever we move towards integration that we can do a better job of it.
"But it is not a question of trying to create a two-tiered approach. It is a graduated response depending on the development of the county team that is in a particular county."
Burns said he will not go looking to the Government for more financial backing in the bid to ease concerns over funding top-level football and hurling teams.
"The GAA doesn't like running to the government for money," he stressed.
The GAA chief said he has a lot of sympathy for Dr McAleese following the resignation.
"I feel really sorry for her in many respects," he revealed.
"We approached her to take us on this journey. She didn't come to us and say that she wanted to do it.
"And I've said to her many times at meetings, 'Mary, I know this must be really frustrating for you, but please just be patient because we have to get consensus of our members before we do anything’.
"I have the utmost respect for her. I think she did really, really well, outstandingly well as chair.
"I will miss her personally because outside of the meetings, she always gave me great insights and great wisdom, which I always benefited from.
"I think the timelines actually held us back more than anything else because we seem to be racing towards timelines.
"Because you have to remember that when we do it, we will be voting two wonderful organisations that have served so well, LGFA and Camogie Association, into oblivion.
"We have to make sure that we do it in a way that respects the structures of both of those organisations and makes them feel they can be a full part of it."
Camogie Association president Brian Molloy praised the work carried out by McAleese, but he also warned that integration won't provide facilities for female players overnight.
"Mary McAleese has done remarkable work for Ireland and, since 2022, has done a remarkable job for the integration process and for Gaelic Games as a whole," said Molloy, the first male president in the 118-year history of the association.
"I commend also her bravery in taking the stand that she has taken.
"The integration moment itself does not either add or remove a single additional facility. We need more facilities anyway and that had nothing to do with integration."
