Taoiseach Leo Varadkar has said he believes Sinn Féin MPs should take up their seats at Westminster before next month's vote on the proposed Brexit deal.
Mr Varakdar said that for "different reasons, Sinn Féin is not participating in parliamentary democracy in Westminster or Stormont".
He said if they are not willing to take up their seats, or feel they cannot because of their policy on abstention, "they do have the option of resigning", to allow people in the seven constituencies in question to decide whether or not they want to "have a say" when the vote comes to Westminster.
The Taoiseach also said the Brexit deal agreed between the UK and EU at the weekend was the "best deal that was available to the United Kingdom".
But he said whether or not they accept it "is a decision for the British parliament".
He said: "We don't want to do anything counterproductive by being seen to interfere in what is a decision for British parliament.
"You can imagine the reaction that might happen in Ireland if you had politicians from Spain or Britain or Denmark coming to Ireland to tell us how we should vote when it comes to parliamentary vote."
However he said "what we can do is answer questions if anyone wants to ask us them from the UK and give assurances".
In response to the Taoiseach’s comments, Sinn Féin President Mary Lou McDonald has said the party is the largest nationalist party in the north and has no intention of abandoning its mandate.
"The reality is that the people of 'those constituencies' have already spoken and they chose abstentionist Sinn Féin MPs," Ms McDonald said in a statement.
The Sinn Féin leader said the Taoiseach "needs to catch himself on".
She added that if the Taoiseach and his party think Irish politicians should take seats in British Parliament, they should seek a mandate for that by standing candidates in northern elections, adding that they should stop "hurling from the ditch".
It comes as British Prime Minister Theresa May addressed MPs in parliament following yesterday's summit in Brussels which saw the UK and EU agree a Brexit deal.
The deal must be put to a vote in the Commons in a little over two weeks' time, and Mrs May said that no one knows what would happen if the deal is not passed.
She has said that it is the best agreement Britain will get.
Earlier, Tánaiste and Minister for Foreign Affairs Simon Coveney said there is no second deal on offer if British politicians decide to reject the Brexit deal agreed yesterday.
Speaking on RTÉ’s Morning Ireland, Mr Coveney said that two years have been spent ensuring that there is no return of a hard border on the island of Ireland and it would be "very foolish" not to use the agreed solution.
Mr Coveney said the backstop solution does not undermine the integrity of the United Kingdom as a whole, including Northern Ireland, but offers the best of both worlds for Northern Ireland.
Mr Coveney said the Government continues to work on a contingency plan, in case of a no-deal Brexit.
Mrs May told a news conference in Brussels yesterday that MPs had the power to open the door to a brighter future by accepting the deal or creating more division and uncertainty by rejecting it.
With her partners in government - the DUP - saying they will vote against it as well as a large cohort of her own party rejecting it, Mrs May has a significant battle to gather the votes she will need.
She has vowed to tour Britain in the coming weeks as part of a drive to convince voters that this deal is the best option ahead of the UK's departure from the EU on 29 March 2019.
Meanwhile, the Taoiseach has met with representatives from the Orange Order today.
He met with the Grand Secretary of the Orange Lodge, Reverend Mervyn Gibson at Government Buildings to discuss issues affecting its members south of the border.
Rev. Gibson led the delegation of Orange Lodge members from southern border counties to discuss matters of interest to their members including in relation to Protestant schools, infrastructure and culture.
They discussed issues of importance to the Orange Order including education and the cultural needs of Protestant communities in border counties.
Brexit and the draft Withdrawal Agreement were also discussed.
Mr Varadkar and the delegation also discussed further development of the Battle of the Boyne site, the possibility of a 'Williamite Trail' from Antrim to Aughrim, and commemorations for World War II.
The Taoiseach recently became the first serving Irish head of government to visit the Orange Heritage Museum in Belfast in June.
In recent months he has been keen to reiterate his understanding and sympathy for Northern Ireland unionists, using his speeches to reiterate that the Government would respect the Good Friday Agreement.
However, the political positions of the DUP and Mr Varadkar's office have been at odds in recent weeks as the Government backed Mrs May's draft agreement, which the DUP has flatly rejected.
In a statement, the Taoiseach said: "The colours on our flag are white, orange and green in equal measure. Sometimes I feel that we haven't fully lived up to that. The Good Friday Agreement acknowledges that people in Northern Ireland have the right to be British, Irish or both, and accepted as such.
"We should acknowledge that there are many people in our State that feel themselves to be both British and Irish. It's something that we should accept too".
He added: "States can best be judged on how they treat minorities. This visit today is another step in an ongoing engagement between the Government and the Order. We must always keep channels of communication open."
Additional Reporting Martina Fitzgerald, Laura Hogan, PA
