"We have Ireland backed by 26 member states and by the [European] Commission; this will not change", he added.
European Council President Donald Tusk will not take part in the meeting.
"We call on the UK Government in its forthcoming white paper to commit to staying inside the single market and customs union recognising that this will require continued alignment with the EU regulatory environment".
Irish economy still growing substantially but Brexit is "a major threat", says Ireland's Central Bank High levels of household and public debt also cause for concern Ireland's economy is still showing strong growth but Brexit poses major risks, according to the country's Central Bank.
The future of the border between European Union member Ireland and Northern Ireland after Brexit is one of the most hotly contested issues in the negotiations, with many on both sides of the border wanting to keep the current free-flowing frontier open.
Wary that a withdrawal treaty might not be agreed in time, time, the European Union leaders said governments should brace for the worst.
The President of the European Commission will address a joint sitting of the Dáil and Seanad this morning.
Coming a week ahead of a key European Council meeting of leaders in Brussels, the visit to Dublin of Mr Juncker and the EU's chief Brexit negotiator Michel Barnier is a clear demonstration of the EU's solidarity with Ireland's position.
Yesterday the European Parliament's chief Brexit co-ordinator told MPs the United Kingdom plan for a temporary customs backstop was "not acceptable" and any fall-back option could not be time-limited.
The EU hopes a final version of the withdrawal agreement, together with a political declaration on the future relationship between London and the EU, can be approved by October so that it can be ratified by the Brexit deadline of the end of March 2019.
Barnier will present the state of play of the negotiations to the European Council on June 28 and 29.
Advances have been made in a number of areas, such as customs, Value-Added Tax and nuclear waste regulation, European Union chief negotiator Michel Barnier has said, but "a lot more work" needs to be done to meet the October deadline.
But there will be no withdrawal agreement without a fully operation backstop.
The pair gave a joint press conference in Dublin as Brexit talks remain stuck over the Irish border question.
Tomorrow he will meet Irish President Michael D Higgins and visit the home of the Gaelic Athletic Association (GAA), Croke Park, and the GAA museum.
"Mr Juncker's claim that "Ireland is not alone" is false security for the country which would be most severely impacted by a no deal Brexit", said DUP deputy leader Nigel Dodds.