The Taoiseach told a Fianna Fáil party meeting last week that he had a positive engagement with British Prime Minister Boris Johnson.
Micheál Martin said the focus is on the resolution of the outstanding issues around the Northern Ireland Protocol.
Ensuring Northern Ireland has access to the single market with minimal checks is important, he said.
The Taoiseach said there was a genuine willingness on the EU side to resolve this through negotiation.
“During our call, I told him it remained my view that every effort should be made to secure a successful outcome to the current EU/UK negotiations.”
Since leaving the EU last year, Britain has delayed the introduction of some checks that were designed to avoid the need for a hard border on the island of Ireland.
Downing Street said the checks are disproportionate and threaten Northern Ireland’s 1998 peace deal.
A spokesperson for Boris Johnson said the British Prime Minister “raised his ongoing concern about the substantial distance between the UK and EU positions” on issues with the protocol when he spoke to Micheál Martin today.
However, the Minister for Foreign Affairs, Simon Coveney, said he believes there is a “window of opportunity” for Britain and the European Union to reach agreement on Northern Ireland trade rules.
“I believe … there is an opportunity before us now to seize momentum towards agreeing a constructive way forward through compromise and partnership,” Mr Coveney told the Seanad Brexit committee.
“I believe the remaining issues can be resolved,” he said. “However, to do so we need to get a much more positive, a much more stable and much more trusting EU-UK relationship.
“We have some way to go to get there.”
Mr Coveney told the committee that Northern Ireland was better off with the protocol.
“Northern Ireland has this unique opportunity to access a very large UK single market, but also a much larger EU single market.
“There is potentially a pull factor into Northern Ireland in terms of foreign direct investment – if the protocol was stable and predictable you could access both markets from Northern Ireland.”
Asked to give an update on the current negotiations, Mr Coveney said there had been a “change in tone” from the UK two weeks ago.
He added: “This certainly suggested to the EU that negotiation was worth investing in, because before that really the negotiations were going nowhere.
“I am more hopeful than I have been.”
He added: “There’s still quite a big gap between the two sides, but at least the negotiations are focused on trying to find landing ground.”