Update 12.30pm: Taoiseach Leo Varadkar has paid tribute to Europe for "transforming Ireland".
"For us, Europe enabled our transformation from being a country on the periphery of the continent to an island at the centre of the world, at the heart of the common European home that we helped to build," Mr Varadkar said.
"The greatest challenge we face on this island is to unwrap the enigma, and solve the riddle of Brexit.
"It's as tricky as it sounds, so we are grateful for the diligence and understanding shown by the Commission's lead negotiator, Michel Barnier, in his conduct of these very difficult negotiations for the EU.
Watch proceedings in the Dail in the embed below or follow the link
Mr Varadkar thanked Mr Juncker for his words of support.
"We are so deeply grateful for the remarkable solidarity and support we have received from the EU institutions and fellow member states, none more so than from President Juncker," Mr Varadkar said.
"There has been consistent recognition of the unique position of Northern Ireland, and the unique situation in which it has been put by the decision of the UK to leave the EU.
"There is no stronger evidence of how small countries benefit so much from EU membership and how membership matters."
Mr Varadkar added: "The moral and political compass of President Juncker has helped to provide direction for Europe, creating more opportunities for our citizens and a better future for all."
Update 12.20pm: Ireland's border is Europe's border
European President Jean-Claude Juncker started his address to - the Oireachtas - by joking he would prefer to be drunk.
He then spoke of his fondness for Ireland, saying over the years he has spent some emotional times in Dublin, recalling, in particular, the summit in 1996 over the single currency.
Mr Juncker has restated his commitment to Ireland as the deadline to Brexit approaches.
"Sometimes at the European Parliament, some of the members there are saying that this is not our business but that this is a bilateral business between Ireland and the UK - we do not share that view.
"We wanted to make it clear again and again that Ireland is not alone. We have Ireland backed by 26 member states and by the Commission - this will not change. I am strongly against any temptation to try to isolate Ireland and not to conclude a deal on Ireland. Ireland has to be part of the deal."
There was applause in the Oireachtas when Mr Juncker restated his commitment to Ireland.
"Ireland will come first... there are those that think the other 26 countries will abandon Ireland for a deal that suits them.
Referring to the UK's imminent departure from the EU, Mr Juncker told the Oireachtas that there is no deal as good as membership of the EU.
"It simply does not exist," he said, adding that the prospect of the UK leaving the EU without any deal at all must be prepared for.
Update 11.30am: Varadkar warns Theresa May 'there isn't much time left'
Taoiseach Leo Varadkar has warned British prime minister Theresa May "there isn't much time left" to agree a workable Brexit just a week out from a crucial European Council summit meeting.
Speaking at Government Buildings alongside European Commission president Jean Claude Juncker, Mr Varadkar said the reality is Britain has yet to resolve the Irish border stand-off and that nothing will happen until this is addressed.
In recent weeks the planned June European Council summit deadline for Britain to provide a clear Brexit plan has effectively been pushed out until the next summit in October.
However, Mr Varadkar said on Thursday morning that time is running out for Britain to address the matter.
"At our meeting [between Mr Varadkar and Mr Juncker] we were in full agreement that there is now an urgent need to intensify our efforts if we're to get there.
"We'll be discussing this further at the European Council meeting next week and our EU partners are absolutely steadfast in their backing for us," Mr Varadkar said.
Latest: The Tánaiste has warned the UK there will be no Brexit withdrawal deal without an agreement on the Irish border.
Ahead of a visit by European Commission President Jean-Claude Juncker to Dublin, Simon Coveney indicated that a no-deal scenario was now being seriously contemplated within the EU.
"This is a question many people are asking," he said.
Simon Coveney says Brexit talks must intensify over the summer, particularly on the border issue pic.twitter.com/JVeflJMP31— RTÉ News (@rtenews) June 21, 2018
Mr Coveney said the EU was standing firmly behind Ireland and its demand for legally binding assurances from the UK to ensure no return to a hard border on the island.
"We have been reassured over and over again that Ireland will not be left isolated here," he said.
Mr Coveney added:
Mr Juncker will be in Dublin on Thursday and Friday as the impasse between the EU and the UK over the border continues.
Coming a week ahead of a crunch European Council meeting of leaders in Brussels, the visit is a clear demonstration of the EU's solidarity with Ireland's position.
This week the EU warned that more work was needed on how to deal with the 300-mile border between Northern Ireland and the Republic, the UK's only land frontier with a European state, and protect frictionless movement after the withdrawal.
Earlier: The President of the European Commission will visit Dublin on Thursday and Friday amid serious differences with Britain over the future of the Irish border.
Jean-Claude Juncker will discuss Brexit ahead of this month’s European Council meeting of leaders in Brussels.
He will address a joint sitting of the Dáil and Seanad this morning.
Mr Juncker will be joined by the EU's Chief Brexit negotiator Michel Barnier.
It is being seen as a gesture of solidarity ahead of next week's European Council meeting
This week the EU warned more work was needed on how to deal with the 300-mile border between Northern Ireland and the Republic, the UK’s only land frontier with a European state, and protect frictionless movement after the withdrawal.
Mr Juncker will meet Taoiseach Leo Varadkar, receive an honorary doctorate from the National University of Ireland and attend an official dinner hosted by the Taoiseach in Dublin Castle.
On Friday the Commission President will meet President Michael D Higgins and visit the home of the GAA, Croke Park, and the GAA museum.
He will also watch a demonstration of Gaelic football and hurling.
Rules governing the border post-Brexit represent one of the most vexed issues facing the negotiators in Brussels.
Advances have been made in a number of areas, such as customs, VAT and nuclear waste regulation, EU chief negotiator Michel Barnier has said, but “a lot more work” needs to be done to meet the October deadline.
Mr Juncker will be accompanied by EU agriculture commissioner Phil Hogan and Mr Barnier.
Later this morning Mr Juncker will address the Irish parliament, the Oireachtas.
Mr Varadkar has suggested other countries will baulk at signing trade deals with the UK post-Brexit if British Prime Minister Theresa May fails to honour commitments made to the EU on the Irish border issue.
Both sides have agreed to include a so-called “backstop” option in the withdrawal treaty, which would commit the UK to align with an EU regulatory framework in the absence of a wider trade deal.
But the shape of that fallback remains a sticking point, with the EU rejecting a UK contention that it should only be temporary, even if a broader agreement fails to materialise.
Britain’s plan for a temporary customs “backstop” is “not acceptable” and any fall-back option cannot be time-limited, the European Parliament’s chief Brexit co-ordinator has told MPs.
Guy Verhofstadt said the British government’s position that the backstop of continuing UK alignment with the EU customs union would cease by the end of 2021 if no other solution was found left him “puzzled”.
The Taoiseach said: “I’m very much looking forward to President Juncker’s first visit to Ireland as Commission President.
“I will thank President Juncker and Michel Barnier for their ongoing support for Ireland and their show of solidarity throughout the Brexit negotiations.
“This is an important opportunity to assess the state of play in the Brexit negotiations.
“We need to see much more progress from the UK to implement the commitments they made in December and March, and I expect the UK’s efforts to intensify in the period ahead.”
He added: “President Juncker and I are both very committed to the European project and the benefits that it brings to citizens across the Union.
“We will also discuss other key items on the agenda of next week’s meeting of the European Council such as trade, ensuring a stable euro, and equipping the Union with a budget for its future needs.”
- Press Association and Digital Desk