The Taoiseach has warned the process will go on "for a very long time"
The Taoiseach Leo Varadkar has said there is "no clean break" on Brexit, but he remains hopeful of a deal.
He was speaking at a meeting of the British Irish Council (BIC) on the Isle of Man.
The British government was represented by Minister for the Cabinet Office David Lidington, as well as the Secretary of State for Northern Ireland Karen Bradley.
Scotland, Wales and the Channel Islands were represented by their heads of administration.
Mr Varadkar also held bilateral talks with Welsh First Minister Carwyn Jones, who was attendeding his last BIC Summit before he steps down.
Brexit, the Common Travel Area and relations with the EU were discussed.
The council also talked about the current political situation in Northern Ireland.
The Taoiseach expressed regret that, until the Stormont Executive is restored, Northern Ireland is without political representation.
In a post Brexit world, forums like the British Irish Council will become even more important. It is very unfortunate that there are no representatives here today from Northern Ireland, due to the lack of a functioning Northern Executive.— Leo Varadkar (@campaignforleo) November 9, 2018
The meeting came as a DUP MP accused British Prime Minister Theresa May of a "total betrayal", amid suggestions a plan for a customs border down the Irish Sea could yet be included in a Brexit deal.
Sammy Wilson attacked Mrs May following the emergence of leaked letter from her to DUP leader Arlene Foster and her deputy Nigel Dodds.
In extracts published by The Times Ireland edition, the letter referred to EU demands for the proposed Brexit backstop arrangement to avoid a hard border in Ireland.
This would apply if a future EU-UK trade relationship failed to avert a hardening of the frontier between the Republic of Ireland and the North.
Asked about his thoughts on this letter, Mr Varadkar said: "I'm a third party in that particular conversation, so it's probably best for me not to speak on behalf of the prime minister or the DUP - they're very much able to speak for themselves.
"But I do think when it comes to Northern Ireland, it's very important to listen to and have regard to what the DUP has to say - but there are other political parties as well who represent the majority of people in Northern Ireland.
"And there's Northern Ireland business, and Northern Ireland farmers and people live in Northern Ireland - I think we really have to have regard to that as well in coming to any conclusion".
"The position of the Irish Government has always been that we don't want to see any new borders between us.
"That applies as much between Larne and Stranraer, or between Belfast and London as it does between Newry and Dundalk or Derry and Londonderry.
"We're not the ones here seeking any borders or any new checks of any sort.
"But Brexit has given risen to a difficult situation and we need to resolve it."
Mr Varadkar also said he was hopeful a deal can be done before the end of this year.
"I'm hopeful that it can be done in the next few weeks - I think it's more likely than not that we will be able to include an agreement in the next few weeks before the end of the year.
"But lots of things can go wrong - and even if we can agree before the end of the year, bear in mind what's agreed will have to be ratified in Westminster, it'll also have to be ratified by the European Parliament.
"And even when all of that is done, then we begin the talks on the future relationship - so there's no clean break here.
"Brexit is going to go on for a very long time".