Taoiseach Micheal Martin has arrived in Belfast for a meeting with Stormont First Minister Arlene Foster and Deputy First Minister Michelle O’Neill.
Discussions at Stormont Castle were due to last for 45 minutes.
This is the Fianna Fail leader’s first official trip to Northern Ireland since the coalition Government he heads was formed last month.
Mr Martin has faced an eventful start to his premiership and sacked his former agriculture minister following drink-driving revelations.
The Stormont leaders had a public falling out over Ms O’Neill’s attendance at the funeral of veteran republican Bobby Storey in west Belfast.
They stood side by side as they greeted the Irish premier on the steps of the building on Thursday.
Mr Martin wore a mask which he removed upon exiting his vehicle.
Later this afternoon he will meet other Northern Ireland party leaders including the SDLP’s Colum Eastwood at the nearby Stormont Hotel.
Mr Martin and the two Northern Ireland leaders discussed Brexit, the Covid-19 response and the New Decade, New Approach deal that restored powersharing in January.
They also agreed to hold a plenary meeting of the cross-border North South Ministerial Council on July 31.
The body co-operates on areas like the environment and waterways.
Mrs Foster said: “I told the Taoiseach that I am keen to have positive dialogue during his tenure based on mutual respect for both jurisdictions and understanding of each other’s differences.
“I look forward to continuing that engagement in the future for the benefit of the people who live here.”
She said recovery from the coronavirus pandemic was a key focus of their conversation as they work simultaneously to protect people and rebuild their economies.
Ms O’Neill said they spoke about the potential implications of Brexit.
She added: “It is now six months since the restoration of the Executive and I made clear to Micheal that we must see delivery of all the Irish Government’s commitments in New Decade, New Approach.
“I look forward to working on a north-south basis to ensure those crucial funding and practical commitments are fulfilled as soon as possible.”
The Deputy First Minister said there were logical reasons to make face coverings mandatory to dampen the spread of coronavirus and added that Stormont ministers would discuss the matter further.
She said: “The chief medical officer (Dr Michael McBride) has made it very clear that while perhaps at one stage of this pandemic he was not convinced of the merits of face coverings, we are now in a space where he thinks that is the case.
“We will look at all of that evidence and then make a decision on that but I think that as more and more people are moving around as we come to the end of the shielding period, there is probably a logical reason as to why face coverings should be a thing that we are all (forced to wear).”
She briefed the media without Mrs Foster after the meeting but said they had “moved naturally” from the days of appearing alongside each other at daily Covid-19 press conferences.
The Sinn Fein vice president added Northern Ireland’s policies needed to be aligned with the Republic’s to minimise the spread of Covid-19, and the jurisdictions’ chief medical officers were working closely together.
She pledged to co-operate well with a Taoiseach who is co-guarantor of the Good Friday Agreement and its institutions despite her party assuming the role of opposition in Dublin’s Dail parliament.
Ireland has delayed the reopening of all pubs in a pause of its easing of lockdown.
Ms O’Neill said: “We have come a long way and our community transmission is very low but we want that to stay the case.”