The Minister for European Affairs has said the draft guidelines agreed today by the European Union's General Affairs Council are robust and recognise Ireland's unique circumstances.
Speaking on RTÉ's Drivetime, Dara Murphy said "I would be very optimistic that the Irish ambition for these talks will be converted into European ambition without qualification. In other words, there is no area where we have failed and the EU, as 27, will now take our concerns as their own and go into the negotiations."
Mr Murphy said there was added reference about the geographic position of Ireland for goods travelling from the UK to the rest of Europe.
He also said there is a specific reference that Northern Ireland would be part of the EU in the event the people of Northern Ireland vote for a united Ireland.
Earlier a senior Government source said all indications so far are that the other 26 members who are remaining in the EU have agreed on Ireland's position as set out in the draft guidelines for the Brexit negotiations.
The senior source said at present there were no significant changes to the guidelines regarding Ireland and this had been viewed as a significant success for the Irish case.
The guidelines have yet to be finalised and the leaders of the 27 remaining European Union states will meet this weekend to sign off on the final negotiating position for the bloc.
The draft negotiations published at the end of last month acknowledge the peace process will remain of paramount importance.
It also states that "in view of the unique circumstances on the island of Ireland, flexible and imaginative solutions will be required, including with the aim of avoiding a hard border, while respecting the integrity of the Union legal order."
It goes on to say the EU should also recognise existing bilateral agreements and arrangements between the United Kingdom and Ireland that are compatible with EU law.
The source also said most of the other EU members that had sought special insertions into the guidelines have not been successful so far.
The Government source said the Good Friday Agreement was the legal and constitutional agreement underpinning the future of Northern Ireland.
Asked about reports that unprecedented measures for Ireland have been agreed in draft EU Brexit documents ahead of this weekend's summit, Mr Kenny said he hopes the summit at the weekend will approve a base document.
Mr Kenny added that the priorities for Ireland have already been identified in the letter from Theresa May to Donald Tusk, the European Parliament paper and the European Council's own proposals.
He said that base document will be followed by a number of other more detailed issues with language around them that will be for approval towards the middle of May.
He is grateful for all the work done by ministers, ambassadors and permanent representation in Brussels, as well as civil servants, he added.
He said it is good to note it is in the draft documents; he wants to see it concluded from that point of view.
Bruton: Brexit will do 'incalculable damage'
It comes as former taoiseach John Bruton said the terms for Brexit set out by British Prime Minister Theresa May "will do incalculable damage to this island, politically, emotionally and economically".
Addressing the Seanad's special Brexit committee, Mr Bruton also said he believes that Britain may decide not to leave the EU or rejoin it at some stage in the future.
He said: "While I believe it may seem impossibly optimistic today, I believe conditions can be envisaged in which, eventually, the UK voters might either decide, either not to leave the EU at all, or to decide, after it has left, to rejoin. Ireland should try to keep that possibility alive.
"The terms for Brexit, as set out so far by Mrs May, will do incalculable damage to this island, politically, emotionally and economically.
"We cannot simply wait for this to happen. While seeking to mitigate the effects of Mrs May chosen hard Brexit, we must also do everything we can to ensure either that, at the end of the day, there is no Brexit."
He cited comments from Mrs May that "no deal at all would be preferable to a bad deal" and said Ireland would be the EU country that would suffer most from the "no deal" scenario between the UK and the EU.
Mr Bruton said "no deal" would mean the UK simply crashing out of the EU overnight, sometime before the end of March 2019. This "no deal" scenario could lead to an overnight halt to flights, to trade and to commerce. There would be immediate, massive currency instability, he said.
On Brexit, Bruton says the "no deal" scenario could lead to an overnight halt to flights, to trade and to commerce pic.twitter.com/sPzy7dd1JV
— RTÉ News (@rtenews) April 27, 2017
Separately, former cabinet minister Dermot Ahern expressed concern over Ireland getting caught in a "crossfire between the UK and the wider EU".
Mr Ahern also told the committee that Ireland needed to maintain its right to decide what is best for its people.
He said nothing was agreed until everything was agreed.
The former minister for foreign affairs said hard bargaining came down to the wire and the interests of individual member states - especially smaller states - could be "conveniently glossed over" if the ultimate price of an agreement was in sight.
He warned that Ireland could lose out in the Brexit negotiations, unless a very hard bargaining stance was adopted from the start.
Meanwhile, the committee heard that a hard Brexit could "seriously undermine the sense of security and acceptance of Irish identity" for Northern Irish people who hold Irish passports.
Michael Farrell of the Irish Council for Civil Liberties said, "Cross-border links and the familiarity they have created has "lessened tensions within Northern Ireland and created an atmosphere of greater normality and a sense that there is nothing inherently threatening to other people in holding Irish citizenship nor something that should be frowned upon."
"If Brexit results in a hard border or the establishment of immigration or other hard border controls, it would seriously undermine the sense of security and acceptance of Irish identity that has been created by the acknowledgement of the right to hold Irish citizenship.
"It could rekindle a sense of isolation and alienation among those holding an Irish identity in Northern Ireland."
He added, "I am not trying to be melodramatic, and I am not suggesting that it could lead to a resumption of the armed conflict, but it could undermine the institutions set up in the North, which are already in considerable dispute.
"The undermining of the valuable solace that recognition of citizenship has given to a part of the community there could contribute to instability and could worsen the divisions there.
"It would also undo the effect that I have mentioned of the growing cross-border links that have developed over the last 20 years," he said.