Update - 1.20pm: The Government says it notes with regret the UK's decision to trigger Article 50.
In a statement this afternoon, the Government said significant preparations have been undertaken to limit the damage that could be caused by Brexit.
The statement says Ireland is negotiating from a position of strength as part of the EU team.
The statement in full said:
Prime Minister Theresa May has today, in accordance with Article 50 of the Treaty on European Union, formally notified the European Council of the UK's intention to leave the EU. This means that the two-year exit process has now commenced.
Although we regret the UK's decision to leave the EU, it has been clear since the referendum last June that the British Government would follow this path.
As outlined in the statement issued today by President Tusk on behalf of the EU 27 Heads of State and Government, negotiating guidelines will now be prepared and, following discussions at Ministerial level, the European Council will meet on 29 April to agree them.
The guidelines will outline the main issues to be addressed in the withdrawal negotiations, and the principles and approach of the EU side.
A more detailed negotiating mandate for the European Commission will be agreed by Ministers in May, and the negotiations with the UK will begin.
It should be noted that the UK will not actually exit the EU until the Article 50 negotiations are concluded, and a withdrawal agreement enters into force. In the meantime, nothing will change, including the UK's obligations towards the citizens and businesses of other Member States.
While the Article 50 exit negotiations should also involve discussion of the future relationship between the EU and the UK, the many important issues involved are unlikely to be resolved for a considerable time.
It has been clear from the start that the UK's departure from the Union will have significant economic, political and social implications for Ireland.
The Government has been working very hard for more than two years, even before the UK referendum, to engage with all sectors across the island of Ireland, to fully analyse our main areas of concern, and to develop our negotiating priorities.
These are to minimise the impact on our trade and the economy; to protect the Northern Ireland Peace Process, including through maintaining an open border; to continue the Common Travel Area with the UK; and to work for a positive future for the European Union.
We note that our particular concerns, including in relation to the Good Friday Agreement, have been acknowledged by Prime Minister May in her letter.
Now that Article 50 has been triggered, we will publish, before the European Council meeting on 29 April, a consolidated paper providing more detail about our priorities and our approach to the negotiations ahead.
We have been extremely active at both political and official level in engaging with every one of our EU partners and with the EU institutions, raising awareness of the unique circumstances in relation to Ireland, and the need to address these in the negotiations. It has also been invaluable to gain a first-hand sense of the objectives of others. We are confident that this intensive engagement has had a very positive impact.
There is no doubt that the negotiations ahead will be very challenging. We have already taken important steps to prepare our economy, including in Budget 2017, the Action Plan for Jobs 2017, and our New Trade and Investment Strategy. The Government's enterprise agencies will continue to work with exporters and potential investors, helping them to deal with issues as they arise - making companies lean, diversifying market exposure, and up-skilling teams.
Ireland is well prepared for the challenges ahead. We will negotiate from a position of strength as an integral part of the EU 27 team, and will work with all our partners to achieve the best possible outcome.
The Irish Tourist Industry Confederation (ITIC), the umbrella group for the tourism industry in Ireland, warned that the impact of Brexit is already damaging Irish tourism.
The latest data from the Central Statistics Office (CSO) confirms that British tourism arrivals to Ireland are down 6% for the period December-February. This represents 49,200 fewer British visitors compared to the same period last year.
Earlier: Fianna Fáil have said Fine Gael's dilemma of a leadership change in the coming months will disrupt the negotiating position of Ireland during initial talks on Brexit, writes Juno McEnroe of the Irish Examiner.
Speaking ahead of London triggering Article 50 and its divorce from the EU today, the party's Brexit spokesman, Stephen Donnelly, also warned of the need to prioritise protective measures for businesses.
Mr Donnelly reiterated that the Department of Finance had warned that a hard Brexit coud cost Ireland 40,000 jobs and add €20bn to our national debt.
Speaking in Leinster House, the Wicklow TD outlined concerns about jobs in the agri-food sector. His colleague Charlie McConalogue said that 25% of milk here came from the North and warned of the instability with fears of a fresh border.
An early transitional deal for trade was needed and Ireland should push for this while the divorce talks between Brussels and London continue, stressed Mr Donnelly.
Government needed to engage with enterprise and, move to protect peace funds in the North and there might only be a year to negotiate on Brexit-once talks end on the €60bn bill that Britain must pay for leaving the union, said Mr Donnelly.
Asked by the Irish Examiner whether the issue of Mr Kenny leaving the talks and being replaced for Ireland was a problem, the TD said: “The Fine Gael leadership issue is a real problem when it comes to Brexit. Who leads Fine Gael is none of our business.
“However, we have been calling for Brexit minister for some time.
"They [Fine Gael] have just thrown him out of the boat. He's going to stay on until June, which mean a leadership election and maybe a new leader by July or August, so there's a reshuffle, maybe we have a new Cabinet in place August, September. The most diligent minister in any party will take several months to read into a brief.
“And so we are well into negotiations before there is continuity of leadership on Brexit from the Irish side.”
He reiterated Fianna Fáil's calls for a Brexit minister to be appointed to head up Ireland's team for Brexit.