The Taoiseach has said it is imperative to protect the institutions of the Good Friday Agreement and make sure they work for all the people on the island of Ireland and for all the islands that are represented on the British Irish Council.
He was speaking following a meeting of the British-Irish Council in Co Fermanagh.
Micheál Martin said there have been many "twists and turns" and everyone has a desire to keep institutions in place.
"From our perspective we believe the mechanisms exist within the Withdrawal Agreement and the protocol to facilitate a working out of these issues.
"There are issues to be refined and resolved and we acknowledge that, but we believe the mechanisms within the framework agreement facilitate that. I think there is opportunity within that framework to resolve this.
"I think discussions should pick up momentum, they did it before prior to the Brexit deal being signed off so, in my view, it is in the capacity of both the UK government and the European Union to arrive at an agreement here.
"Ireland, as members of the EU, we have appraised people of the sensitivities of all of this, we want to be helpful. I do think there is potential."
Mr Martin also said he believes the interest from US President Biden has been "overall, beneficial" to the peace process.
At the British-Irish Council press conference, Taoiseach Micheál Martin set out the direction in which he believed EU-UK discussions should go to resolve issues around the Northern Ireland Protocol | https://t.co/CHWk4FdeP1 pic.twitter.com/pFSzBJX6UD— RTÉ News (@rtenews) June 11, 2021
"He sees the UK, US and the EU as aligned on fundamental issues," he said, adding that Mr Biden "wants to see issues resolved and his suggestion has been a helpful one".
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NI First Minister Arlene Foster says there was a "very good discussion" around Covid-19 and recovery at the British-Irish Council meeting. Deputy First Minister Michelle O'Neill said it was a "very timely discussion" | https://t.co/CHWk4FdeP1 pic.twitter.com/kZ14FQCEmY— RTÉ News (@rtenews) June 11, 2021
Northern Ireland First Minister Arlene Foster said the British-Irish Council meeting is an "important part of the Belfast Agreement".
She said a "very good discussion"' had taken place around Covid-19 and recovery and "how we each embark on that journey".
Deputy First Minister Michelle O'Neill said it was a "very timely discussion as we work our way out of Covid-19 and very productive conversation and [we] look forward to continuing crucial work across Ireland".
Ms O'Neill said that everyone wants to make powersharing work and it has to be good for everyone and on the basis of respect for everyone and "making politics deliver for everyone".
The Taoiseach thanked Ms Foster "for her contribution to public life as leader of DUP and before that".
He said it "takes politicians of courage to build bridges and develop effective shared government".
Ms Foster broke into song at the press conference following the meeting, with a line from her favourite Frank Sinatra song, That's Life.
During one of her last official engagements as Northern Ireland First Minister, Arlene Foster broke into song at the British-Irish Council summit with a line from her favourite Frank Sinatra song, 'That's Life' | https://t.co/iuLCtbwVds pic.twitter.com/uSnBrLg7ax— RTÉ News (@rtenews) June 11, 2021
She sang the lyrics: "That's Life. That's what all the people say. You're riding high in April, shot down in May", receiving a round of applause.
Speaking during one of her last official engagements as Northern Ireland First Minister, she added: "I think it's a good way to end my political career at the British Irish Council meeting in Fermanagh because it has absolutely encapsulated the totality of relationships and I am pleased everyone is here."
Taoiseach @MichealMartinTD and Tanaiste @LeoVaradkar have cuppa and chat with @ArleneFosterUK @moneillsf and others ahead of British Irish Council meeting in County Fermanagh @rtenews @LauraHoganTV pic.twitter.com/eLp1OvFZs1— Vincent Kearney (@vincekearney) June 11, 2021
The British government was represented by its former Brexit minister Michael Gove and Northern Ireland Secretary Brandon Lewis, as Prime Minister Boris Johnson is taking part in the G7 Summit in Cornwall.
Scotland's First Minister Nicola Sturgeon and her Welsh counterpart Mark Drakeford joined the meeting
remotely because of Covid-19 concerns in their devolved administrations.
The administrations in Guernsey, Jersey, and the Isle of Man also took part remotely.
Mr Gove said: "Sometimes when people look at the protocol they think it is all or nothing at all. The truth is that the protocol is an arrangement which is developed through dialogue in the joint committee and the specialised committees between the UK government and the European Union.
"We have resolved some of the challenges that have existed but there are other challenges which do need to be tackled effectively.
"I won't go into the detail exactly what an eventual set of arrangements would be, simply just to affirm two things. The first is that the protocol is there to uphold the Belfast Agreement in all its dimensions and it is important that the east-west dimensions are respected.
"The second thing is that I believe there is a willingness within pragmatic figures within the European Union to make sure that we can make these arrangements work so that they do not impact adversely on the lives of people across communities in Northern Ireland and I know that the Irish Government is using its best endeavours in order to proceed in a pragmatic and constructive way."
EU-UK 'tensions strained' - McGuinness
European Commissioner Mairead McGuinness has said "trust is in short supply" on the part of the European Union in relation to the implementation of the Northern Ireland Protocol by the UK.
Speaking on RTÉ's Today with Damien O'Reilly, Ms McGuinness said "tensions are strained" between the European Union and the UK "over what has not happened in relation to the protocol.
"Tensions are very strained at the moment and the word trust being used a bit. It is in very short supply. My colleague Maroš Šefcovic as a former diplomat and he has worked in this area, and even his patience I think is at this stage is quite strained around what's happening, or what is not happening around implementing the protocol."
Ms McGuinness said the EU has proposed solutions to issues in the protocol on plant and animal checks, but she said these have not been met with positive responses from the UK.
"When you sign a treaty you are obliged to implement it and that is what the EU is trying to ensure while at the same time addressing the issues that businesses are dealing with, and trying to find flexibilities."
She said the UK is fully aware of the obligations they signed up to in 2019.
Ms McGuinness said the EU must "be firm" on its requirements, which she said are the sensitivities of Northern Ireland, the island of Ireland and the single market.
Additional reporting Laura Hogan, PA