The Taoiseach has said a no-deal Brexit would be "very bad for all of us" and "an appalling failure of statecraft" from both the EU and the UK.
The deadline for Britain and the EU to reach a trade deal to underpin the post-Brexit relationship between them is midnight.
Both parties continued talking into the night and will continue their discussions today.
British Prime Minister Boris Johnson and EU Commission President Ursula von der Leyen are due to speak on the phone later today at around lunchtime.
Fisheries has been at the top of the list of glaring disagreement, with the EU seeking maximum access for its boats to continue fishing in UK waters.
Britain wants most of that business back, and says it will prioritise its own boats with Royal Navy vessels on standby to patrol UK waters.
The second issue related to rules on fair competition and the level playing field.
Speaking to the BBC today, Micheál Martin said a no-deal scenario "would be very bad news for all of us".
He added: "I think it would be an appalling failure of statecraft if we were not in a position to get a deal over the line.
"For Ireland and also for UK and EU member states. We are interdependent.
"My view is that it is absolutely imperative that both sides continue to engage and both sides continue to work to negotiate to avoid a no-deal.
“97% of this deal has been negotiated across judicial security research a whole range of areas, and it seems to me that the remaining 3% should not be beyond the capacity of both sides to bridge, and that is why it’s so important that dialogue continues."
He called on negotiators from both sides to focus on reaching a deal "with any bit of energy we have left".
#Marr: Would you say that no trade deal between the UK and EU represents a failure of statecraft by both sides?
Irish PM Micheal Martin: "I would"#Brexit https://t.co/qvhGW845Bt pic.twitter.com/tKPRBc6Goh
— BBC Politics (@BBCPolitics) December 13, 2020
Meanwhile, the British Foreign Secretary has said the EU is "concerned" the UK "might do rather well" after Brexit.
Dominic Raab suggested talks could go on beyond this evening, despite the weekend deadline.
As the clock ticks down to December 31st when the transition period ends, he told Sky News "there is still a long way to go" before an agreement is possible.
Mr Raab added now it is getting to the "eleventh hour" so what needs to happen is "moving the political logjam".