Micheal Martin said the European Union was already dealing with the economic fallout from the Covid-19 pandemic.
He made the comments at the end of a two-day meeting of the European Council in Brussels today.
The Taoiseach said the continued negative impact of Covid-19 on the economic performance across Europe formed a dominant part of the meeting of EU heads of state.
“The last thing we all collectively need now is another hit to the economy occasioned by a no-deal Brexit,” he said.
“It doesn’t make sense and that is the spirit within which people want to approach these negotiations.”
Speaking in Brussels, Mr Martin also said it was highly unlikely that a deal would be struck between the EU and the UK in the next fortnight but that there was a “mood to engage”.
“There is a sense whilst there is a mood to engage, no-one is underestimating the task that lies ahead,” the Taoiseach said.
He added: “I think it’s highly unlikely that there will be any deal by October 15th, by the middle of the month.
“It is fair to say that’s not the timeframe within which now people are looking at the possibility of a deal.
“That said, certainly by the end of the month, the beginning of next month, there would have to be some clear pathway to an agreement in order to facilitate all the work that will then be necessary to get a deal over the line.”
The Taoiseach’s remarks come as European Commission president Ursula von der Leyen called for trade talks with the UK to “intensify” as she prepared to discuss the matter with UK Prime Minister Boris Johnson.
The two leaders are to speak on Saturday to discuss the “next steps” following the conclusion of the final scheduled round of formal negotiations on a post-Brexit trade deal in Brussels.