British Prime Minister Theresa May has turned down an invitation to address the Dáil during her visit to Dublin later this month.
The decision by Ms May comes after the Supreme Court in the UK today ruled that Parliament must vote on legislation to trigger Brexit - but a spokesman for 10 Downing Street has said it will not change plans to trigger divorce proceedings by March.
"The British people voted to leave the EU, and the Government will deliver on their verdict - triggering Article 50, as planned, by the end of March. Today's ruling does nothing to change that," he said.
The Government appealed against a High Court ruling in November which blocked Prime Minister Theresa May using the royal prerogative to launch Britain's exit from the EU without Parliament having a say.
Speaking after the ruling the Attorney General Jeremy Wright said the government will do "all that is necessary" to implement the ruling.
Mr Wright said the Government was "disappointed" by the final decision in its historic battle over who has the right to authorise the start of withdrawal negotiations under Article 50 of the EU treaties.
But he said that ministers will comply with the ruling, which effectively means that MPs must be given a vote on Article 50.
Speaking on the steps of the Supreme Court, the Attorney General said: "The Government will comply with the judgment of the court and do all that is necessary to implement it."
Minister for Foreign Affairs Charlie Flanagan has welcomed the UK Government's remarks.
"I welcome the confirmation from the UK Government that it will proceed with the triggering of Article 50 by the end of March at the latest. This provides welcome certainty for the beginning of the negotiations between the UK and the E," he said.
"The Government's preparations for the upcoming negotiations on the UK's withdrawal from the EU have been extensive and comprehensive. These preparations and our programme of engagement with our EU partners are continuing and we will be ready for the challenging negotiations ahead.
"Our priorities in these negotiations remain our citizens, our economy, Northern Ireland, our Common Travel Area and the future of the EU itself," he added.
The highest court in the UK rejected an appeal by ministers against a High Court judgment blocking their decision to begin Britain's exit from the European Union without Parliament having a say.
Supreme Court justices ruled, by a majority of eight to three, that Ms May cannot lawfully bypass MPs and peers by using the royal prerogative to trigger Article 50 of the Lisbon Treaty and start the two-year process of negotiating the UK's divorce from its EU partners.
However, they unanimously rejected an argument that devolved administrations in Scotland, Wales and Northern Ireland must be consulted before Article 50 is triggered.
The ruling is a blow to Mrs May, who has repeatedly said she intends to trigger Article 50 by the end of March following the clear majority in favour of Brexit in the June 2016 referendum.
But she will be buoyed by the decision on the devolved administrations, which could have been much more significant in upsetting her timetable if it had gone the other way.
The court case was won by a wide-ranging group of anti-Article 50 campaigners led by investment manager Gina Miller, 51, and hairdresser Deir Dos Santos.
Supreme Court President Lord Neuberger said: "By a majority of eight to three, the Supreme Court today rules that the Government cannot trigger Article 50 without an Act of Parliament authorising it to do so."
Speaking after the ruling, Mr Wright said: "Of course the Government is disappointed with the outcome. But we have the good fortune to live in a country where everyone - every individual, every organisation, even government - is subject to the rule of law.
"So the Government will comply with the judgment of the court and do all that is necessary to implement it.
"The court has been very clear throughout this case that it has not been deciding whether the United Kingdom should or should not leave the European Union.
"The people of the United Kingdom have already made that decision.
"Now enacting that decision will be a political matter and not a legal matter."
The Supreme Court in the UK has ruled that Parliament must vote on legislation to trigger Brexit but a spokesman for 10 Downing Street has said it will not change plans to trigger divorce proceedings by March.