The Taoiseach Leo Varadkar has said there is a "pathway" towards a Brexit deal in the UK.
It comes after he met British Prime Minister Boris Johnson for around three hours on Thursday in Cheshire, England.
In a joint statement afterwards, the two leaders said discussions were "detailed and constructive".
They also "continue to believe" a deal is in everybody's interest.
The talks focused on challenges around customs and consent - they also discussed "the potential" to strengthen bilateral relations.
Officials will continue to engage in discussions and Mr Varadkar will consult with the EU Task Force, the statement added.
— Leo Varadkar (@LeoVaradkar) October 10, 2019
In a press conference following the talks, Mr Varadkar said: "What I can say is that I had a very good meeting today with the prime minister and our teams together - 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, the United Kingdom and the European Union as a whole.
"And I do see a pathway towards an agreement in the coming weeks."
He said outstanding issues include consent and democracy - ensuring any long-term arrangement that applies to Northern Ireland has the consent of the people there.
The second is ensuring there is no customs border between North and South, Mr Varadkar said.
"The next steps of course are for the United Kingdom government to engage with the European Commission - we expect that'll happen tomorrow with a meeting involving [UK Brexit Secretary] Stephen Barclay and Michel Barnier."
He said the Irish Government will consult and meet with the commission as well.
"But what I would hope is that what's happened today would be sufficient to allow negotiations to resume in Brussels".
Asked how long the pathway to a deal would be, Mr Varadkar said he could not predict that "with any certainty".
"I would say a short pathway rather than a long one, but it's impossible to predict that for sure".
Earlier this week, Downing Street accused the EU of making a deal “essentially impossible.”
On Wednesday, the chief EU negotiator Michel Barnier warned that the two sides were not in position to reach a deal.
Meanwhile political commentator in Northern Ireland, Newton Emerson, told The Hard Shoulder why DUP leader Arlene Foster may be thrown under the proverbial bus in the event of an agreement.
The meeting between Mr Varadkar and Mr Johnson was the third between the two leaders since Mr Johnson became UK prime minister.
Last week, Mr Varadkar warned that if the UK wants the backstop removed from the agreement it must come up with workable solutions by tomorrow.
The EU has warned that there are a range of issues with proposals put forward by the UK thus far – notably that they still require customs checks in Ireland and effectively hand the DUP a veto over the arrangement.
Mr Varadkar has noted that the UK has already reneged on the Brexit withdrawal agreement Mr Johnson’s predecessor negotiated with the EU and was now trying to put half of it back on the table and call it a “concession.”
'Take it or leave it'
He said the UKs current ‘take it or leave it’ stance to its proposals poses “great difficulty” for Ireland and the EU.
“As far as the Irish Government is concerned, we do want a deal,” he told the Dáil yesterday.
“We're willing to work hard to get a deal, to work until the last moment to get a deal – but certainly not at any cost.”
Mr Johnson continues to insist the backstop is “undemocratic” and last night his Business Secretary Andrea Leadsom said the UK Government “would not entertain” it in any form.
Mr Johnson has repeatedly insisted he will take the UK out of the EU with or without a deal on October 31st.
However, he is legally obliged to seek an extension – and agree to whatever date he is offered by the EU – if no solution is in place by October 19th.
There are concerns however that he will seek to undermine the request in some way - as his team has suggested it believes he can follow the letter of the law while still taking the UK out on October 31st.
Meanwhile, the UK Labour Party leader Jeremy Corbyn will use a speech on Thursday to warn Mr Johnson that he must avert a no-deal scenario before opposition parties will agree to a new general election there.
“It wasn't long ago that Johnson was pretending not to want an election,” he will say. “Now he is pretending that it's Labour that doesn't want one.”
“So let me address this directly: prime minister, we can't trust you not to break the law because you've got form.
“We can't trust you not to use the period of an election campaign to drive our country off a no-deal cliff edge that will crash our economy, destroy jobs and industries, cause shortages of medicine and food and endanger peace in Northern Ireland.
“So it's simple: obey the law, take no-deal off the table and then let's have the election.”
Additional reporting: Jack Quann and Sean Defoe