The executive parties are to meet later to discuss the political fallout following the funeral of veteran republican Bobby Storey.
Deputy First Minister Michelle O’Neill has been accused of breaching social distancing regulations at the funeral in west Belfast on Tuesday.
Four executive parties including the DUP have called for her to step aside.
It is Stormont’s biggest political crisis since devolution was restored in January after a three-year hiatus.
On Thursday, First Minister Arlene Foster said she cannot currently “stand beside” Ms O’Neill – who is Sinn Féin’s deputy leader – and “give out public health advice” after her attendance at the funeral.
Bobby Storey was a former prisoner and close friend to leading Sinn Féin figures and was considered the head of intelligence of the IRA for a period from the mid-1990s.
Tuesday’s funeral was the latest in a number of events that have been criticised for attracting crowds during the Covid-19 pandemic.
The Democratic Unionist Party (DUP), Ulster Unionist Party (UUP), Alliance Party and SDLP have called for an investigation into Ms O’Neill’s behaviour and believe the executive’s health message aimed at containing Covid-19 has been undermined.
Friday’s meeting will involve Ms O’Neill, the DUP leader Mrs Foster, Colum Eastwood of the SDLP, the Alliance Party’s Naomi Long and Steve Aiken of the UUP.
The party leaders’ forum was established as part of the New Decade, New Approach deal which re-established the power-sharing executive in January.
Sinn Féin insist Ms O’Neill has done nothing wrong and have accused their critics of attempting to score political points.
In a statement, the party said she would not step aside “under any circumstances”.
Speaking in Dublin on Thursday, Sinn Féin president Mary Lou McDonald said Ms O’Neill should not stand down.
“I don’t think anybody should be punished or asked to step aside or step down because they attended the funeral of their friend,” she said.
However, a series of statements from the other executive parties has placed pressure on Sinn Féin to say the scenes from Tuesday’s funeral in west Belfast are a cause for concern.
DUP MP Sir Jeffrey Donaldson said there needed to be an investigation into whether the regulations had been breached.
He said: “We will also be asking the PSNI to specifically investigate any potential regulatory breaches by executive ministers, including the deputy first minister.”
Mr Donaldson said Ms O’Neill “failed to realise the public mood on this and the deep concern that people are taking this personally”.
Current coronavirus regulations state a maximum of 30 people are allowed to gather together outdoors.
About 120 mourners were inside St Agnes’s Church in Belfast for Mr Storey’s funeral, BBC News NI understands.
The deputy first minister told a Stormont committee on Wednesday that Requiem Masses were now possible due to this week’s reopening of places of worship.
However, guidance on religious services issued to faith leaders last week stipulated that it did not apply to weddings, baptisms or funerals.
Updated guidance, seen by BBC News NI on Wednesday and published on the Department of Health website on Thursday, said funeral services could now be conducted in a place of worship.
“The size and circumstances of the venue will determine the maximum number that can attend the service safely whilst observing social distancing of at least 2 metres, wherever possible,” it continued.
“It is recommended that face coverings are used for indoor services.”
The guidance for those gathering outdoors remains the same with the guidance, issued for funeral directors, stating “a maximum of only 30 are permitted to gather for the committal at the graveside or at the front of the City of Belfast Crematorium”.