The coming days are crucial in ending the stand-off on Brexit, with the Government warning the matter must be resolved sooner rather so that the country isn't merely given 24 hours notice "before a cliff edge" of no deal.
Talks will continue this week after British prime minister Boris Johnson and European Commission president Ursula von der Leyen agreed to "go the extra mile".
Micheál Martin, speaking in Cork at the launch of a documentary on hurler Christy Ring, said the coming days are "very, very important" in resolving the issues around the level playing field, dispute-resolution mechanisms, and fisheries.
Simon Coveney, the foreign affairs minister, made similar remarks, adding there is merely a matter of days to resolve the process "because if this is to fail, we can't allow failure to happen with 24 hours to go before a cliff edge".
The Taoiseach welcomed the decision to continue the talks, but warned of the urgency to reach a conclusion.
"It is extremely important and it is imperative that both sides to everything they possibly can to avoid a no-deal Brexit — because a no-deal Brexit would be very damaging all round to the United Kingdom economy, to the Irish economy, to the European Union economy, to workers and businesses who need certainty and who need clarity and I think it is good that they are continuing with the talks.
"It is very important that they do everything they can to get a deal over the line."
Mr Coveney, while welcoming the fact that no deadline had been placed on the next round of discussions, insisted time is at an absolute premium.
He said the Government has been planning for a no-deal scenario for more than 12 months but "it will still be much more disruptive than otherwise is necessary if there isn't a trade deal here, and a future relationship agreement".
"We certainly don't want to see that announcement 24 hours before it actually happens," Mr Coveney told RTÉ'sprogramme.
As the January deadline looms, talks continued over the weekend, but difficulties still remain around fisheries and the so-called level playing field.
Speaking after what she described as a "constructive" and "useful" phone call on the remaining issues, Ms von der Leyen said both sides believe it is "responsible" to continue to try to hammer out a deal.
However, Mr Johnson warned that the UK is still prepared to crash out of the EU without a deal.
Even if UK and EU negotiators manage to hammer out a deal in the coming days, any agreement would still need to be approved in both London and Brussels.
Any agreement would first need to be turned into legal text and translated into 23 EU languages before being signed off on by the European Council, and the European Parliament. It would also have to get through the UK Houses of Parliament.
Asked about the possibility of a scheme for food exporters in the case of a no-deal Brexit, Mr Coveney said the Government "won't be found wanting" in terms of supporting vulnerable sectors.
"The agri-food industry will be one of the areas hardest hit, because we sell €5.5bn worth of food and drink to the UK each year," Mr Coveney said.
"If there are tariffs on that trade, we could be paying tariffs of up to €1.5bn, which would be hugely disruptive and damaging for that market."