The Taoiseach said the British Prime Minister has shown a "genuine desire" to reach an agreement on Brexit.
The historic first meeting between Micheál Martin and Boris Johnson took place on Thursday, at the Hillsborough Castle and Gardens in Co Down.
Continuous reports of stalemate have plagued negotiations for Britain's exit from the EU for months, with officials reporting disappointment with Britain who appear to be shifting from the political declaration already agreed upon, which could lead to a no-trade deal Brexit, with huge ramifications for both Britain and Ireland's economies.
"I took from our meeting, and my engagement with the Prime Minister a genuine desire to reach a sensible, comprehensive agreement," Mr Martin said.
"We both agreed on one thing, Covid has had a very negative impact on our respective societies and economies.
"The last thing we all need now is a second significant systemic shock to our economic systems and that's what a no-deal Brexit, would present on top or alongside Covid.
"There's a lot of work being done at an official level in relation to the protocol, and it is our view that that should continue.
"There's still more work to be done. So, the officials on all sides are working with special responsibility for the details."
Mr Martin said he was "not the referee" between London and Brussels, and refused to be drawn on which officials should be more open to compromise, "I think where there's a will there's a way," he said.
"It seems to me that there is a landing zone, if that will is there on both sides and I think it is on the European Union side.
Productive and warm first meeting with PM @BorisJohnson. We discussed the impact of #COVID19, the evolving approaches to it and supporting the institutions of the GFA. Crucially, we decided to develop a new framework for British-Irish relations in a post Brexit world pic.twitter.com/snleHQyzlj— Micheál Martin (@MichealMartinTD) August 13, 2020
"My own gut instinct is that there's a shared understanding that we don't need another shock to the economic system that a no-deal Brexit would give, or that a sub-optimal trade agreement would give to our respective economies, across Europe and Ireland, and Great Britain itself, alongside of the enormous shock that Covid has already been.
"I think it's it's there, it's a matter of both sides engaging, they will resume talks later this month and I would hope that they can bring about an agreement."
Micheál Martin added that both he and the Prime Minister agreed "to set to work immediately to create structures" around the British-Irish relationship, in terms of economic connections.
"It's absolutely essential that the type of relationships we've built up with members of the European Union are not lost, and that we now look in a visionary way post-Brexit, at how that relationship can be nurtured and developed in a proper structured way too," he said.
"That's the best possible outcome for European Union for the United Kingdom.
"He assured me that the United Kingdom is very committed to reaching a comprehensive agreement with Europe, that would ensure such a free trade deal."
PM @BorisJohnson has held his first meeting with Taoiseach @MichealMartinTD.— UK Prime Minister (@10DowningStreet) August 13, 2020
They discussed the close ties between our countries.
The EU has stated that any deal would need to be done by October to allow time for ratification by the end of the year.
The pair also spoke about the continued role of both governments to support the Northern Ireland executive, the assembly and the institution of the Good Friday Agreement.
"Particularly the fact that in our views since the resumption (of the Executive) there has been good work done, and that we two core guarantors must all work on our commitments on the new technical approach," Mr Martin added.