First Minister Paul Givan has said there is a “window of opportunity” to resolve the issues caused by the Northern Ireland Protocol.
Speaking after a meeting of the North South Ministerial Council (NSMC) on Friday, the DUP MLA also said the Irish Government has an important role in influencing the EU.
Post-Brexit impact on NI
"What we have is a window of opportunity with the UK Government recognising the political societal and economic harm that has been caused by that protocol," Mr Givan added.
"The European Union has now suspended its litigation and there's recognition that the protocol is causing harm, that there needs to be constructive engagement between the UK Government and the European Union.
"Obviously the Irish Government have a very important role in influencing how the European Union conducts its approach to addressing those issues."
Mr Givan further said: "Nobody should be under any illusion as to the implications that the protocol has had, the manner in which it was foisted upon the Unionist community and the way in which there was engagement for the European Union, where we had photographs of border posts being bombed in the 1970s in order to get the European Union on side when it came to this protocol.
"That caused huge damage within the Unionist community, by the way in which the Irish Government at that time engaged in the process, and we want to see a new relationship developed after the out-workings of the UK Government and European Union engagement as a result of this command paper haven't been published."
Sinn Féin deputy First Minister Michelle O'Neill said she raised the issue of Brexit grace periods coming to an end and added that the economic challenges the public face are a direct result of Brexit.
"Those that delivered the hardest possible Brexit have to shoulder some of the responsibility for where we are," she added.
"That being said, I think that within the framework of the Withdrawal Agreement, we have the Joint Committee, that is the forum in which we can iron out some of the issues that need to be resolved.
"Some of which arise because of the lateness of the deal itself, some of which arise because we live in a new trade reality as a result of Brexit.”
Commenting on the meeting which he described as "good, relaxed, engaged and pragmatic", Taoiseach Micheál Martin said the Brexit issues can be ironed out and resolved if the "political will" exists.
"I think there are issues in the protocol that we can work together to try and resolve," he said.
"The British Government and the European Union Commission are engaging in respect of dealing with those issues.
"The British Government has issued a command paper, the EU have responded, the EU has extended the grace periods.
"There has been a lot of work done over the last number of months."
Mr Martin added: "Again, there's obviously more work to be done there, but there is engagement between the UK Government and European Union Commission.
"The Irish Government stands ready to be helpful and has engaged with the commission on these issues and with the UK Government on these issues."
The Taoiseach hosted the 26th plenary meeting of the NSMC, which took place via video conference.
It addressed a range of issues, including the handling of Covid-19 on the island of Ireland as well as the implementation of the New Decade, New Approach agreement.