Taoiseach Leo Varadkar says he believes it is possible to get a Brexit deal by the 31 October deadline following talks with Boris Johnson.
Mr Varadkar was speaking at Liverpool Airport after meeting with the British Prime Minister earlier today.
He told reporters: "I'm sure you appreciate that this is a very sensitive issue and we're at a very sensitive stage at the moment, so I won't be able to go into too much detail.
"I think sometimes at this stage in negotiations and discussions, the less said the better, but what I can say is that I had a very good meeting today with the Prime Minister and our teams.
"It was very positive and very promising. I am now absolutely convinced that both Ireland and Britain want there to be an agreement that's in the interests of Ireland and the United Kingdom and the European Union as a whole, and I do see a pathway towards an agreement in the coming weeks."
Mr Varadkar said that despite the progress there were still issues "yet to be fully resolved", including ensuring that any long-term arrangement applying to Northern Ireland had the consent of the people there.
He said the second issue was to ensure "that there is no customs border between north and south".
"We also had a good discussion looking forward to how relationships might look after Brexit, how we can strengthen cooperation north and south, economically and politically," Mr Varadkar said.
Mr Varadkar said that the next step was for the Britain to engage with the European Commission, which is likely to happen tomorrow when the British Brexit Secretary Stephen Barclay meets with Michel Barnier.
The Taoiseach added that Ireland will also need to "consult and engage" with the Commission.
Mr Vardakar said: "I think all sides would like there to be an agreement next week at the council if possible, and obviously there's a further deadline after that, the 31st of October, so I would say a short pathway rather than a long one."
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He added: "What this is about is securing an agreement that works for the people of Ireland and also the people of Britain and Europe. If it works for the people of Ireland, what it means is, avoiding a hard border between north and south.
"That's always been our primary objective, ensuring that the all-island economy can continue to develop, and that north-south cooperation, envisaged by the Good Friday Agreement, can resume. Those are our objectives, this has always been about achieving those objectives, and I think today they can be achieved."
Earlier, Mr Varadkar and Mr Johnson said they could "see a pathway to a possible deal" following the Brexit talks in Cheshire.
In a joint statement, both leaders said the summit had been detailed and constructive.
According to the statement, the discussions concentrated on the "challenges of customs and consent".
They also discussed the potential to strengthen bilateral relations, including on Northern Ireland.
As a follow up to these negotiations, the Taoiseach is to consult the EU Taskforce 50, while the UK Brexit Secretary Stephen Barclay is to meet with the EU's chief negotiator Michel Barnier tomorrow morning.
Here's our joint statement following my meeting with @BorisJohnson in Cheshire this afternoon pic.twitter.com/RxjF9qFte8— Leo Varadkar (@LeoVaradkar) October 10, 2019
The Fianna Fáil leader Micheál Martin said: "I'm pleased that the megaphone diplomacy has been replaced by proper and serious Brexit discussion today. The signals coming from Liverpool are encouraging and we hope that positive momentum can be sustained over coming week."
Sinn Fein President Mary Lou McDonald said: "The next week is critical, any deal should include the backstop as the bottom line to protecting Ireland, no veto can be given to unionism on protections for Ireland. We'll continue our work with other pro remain parties, Irish govt and EU to this affect."
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Speaking this evening in Dublin, Tánaiste Simon Coveney said it is still possible for a Brexit deal to be done by the end of October.
He told the Dublin Chamber of Commerce that while there had been progress, people "should not get carried away."
He added that the term backstop has become politically demonised, and that if there is another way to achieve the same outcome, the Government would accept that.
Mr Coveney described today as a "positive day", and said it is important to acknowledge that.
"The Taoiseach and the Prime Minister had another very good meeting. As the Taoiseach said on his way home, we can see a pathway now for a possible deal ahead. But I think it's important that we don't get carried away. There is still a significant amount of work to done."
The talks come with time running out to sign off on any agreement at a 17-18 October leaders' summit in Brussels, ahead of the UK's scheduled departure from the EU at the end of the month after nearly five decades of membership.
Mr Johnson has vowed Britain will leave on 31 October with or without a deal, despite MPs passing a law last month that requires him to seek another Brexit delay if he fails to secure a pact at the summit.
Additional reporting PA, AFP