Arlene Foster is expected to appear alongside Sinn Fein vice-president Michelle O’Neill in public on Friday following a meeting of ministers from both sides of the Irish border.
The North South Ministerial Council is being held in Dublin for the first time since devolved government was restored at Stormont in January.
Taoiseach Micheal Martin, the first minister and deputy first minister will gather at Dublin Castle to discuss matters of mutual interest.
Bobby Storey’s funeral is still under police investigation over potential breaches by mourners of social distancing rules.
Mrs Foster said: “I have always made it clear that we need to have the Executive working and need to continue to deal with Covid.
“We need to continue to focus on recovery, dealing with EU exit meetings.
“I have never said that we have not continued to work as an Executive across the five parties together.”
Mrs Foster has said her powersharing partner’s apology after attending the republican funeral “falls short”.
Trust between members of the Stormont coalition and Ms O’Neill’s credibility in delivering Covid-19 health messaging have been damaged by the controversy over large crowds as the cortege passed through west Belfast, the DUP leader said.
Ms O’Neill has stood by her decision to go to the west Belfast service for the senior republican but did say sorry to families bereaved during lockdown for any hurt caused by scenes of hundreds of people lining the route.
The Executive met on Thursday.
Mrs Foster said the Covid-19 tracker phone app launched on Thursday would work in an inter-operable way with the Republic of Ireland and any brought forward by the other UK administrations.
Self-isolation with Covid-19 symptoms or a positive test result has been increased from seven days to ten.
Ministers also agreed to relax Covid restrictions in child care settings by August 1.