Sinn Fein has rejected a DUP call for its Stormont Deputy First Minister to stand down over her attendance at an IRA veteran’s funeral that drew hundreds of people on to the streets.

First Minister Arlene Foster has written to her partner-in-government Michelle O’Neill asking her to step aside pending police and Assembly standards investigations into the scenes at Bobby Storey’s funeral in west Belfast on Tuesday.

The move has plunged the recently restored powersharing institutions into crisis again, with four of the parties in the five-party coalition Executive calling for Ms O’Neill to stand down.

Sinn Fein president Mary-Lou McDonald said Ms O’Neill would not be stepping aside. She said no one should be “punished” for attending the funeral of a friend.

Under Stormont regulations and guidance, friends of a deceased person should only attend the funeral if none of the bereaved family members are attending. Mr Storey’s family did attend Tuesday’s funeral.

Mrs McDonald said the Stormont Executive should keep focused on work to tackle the Covid-19 emergency.

“That work is under way but it is not finished yet, so, no, I don’t think anybody should be punished or asked to step aside or step down because they attended the funeral of a friend. No, I don’t,” she said.

Thursday’s scheduled Stormont press conference on the coronavirus emergency with Mrs Foster and Ms O’Neill was cancelled due to the row.

The events have some echoes of the cash-for-ash furore that toppled the devolved government in 2017 when Mrs Foster refused to accede to a Sinn Fein call for her to temporarily stand down pending an investigation into a botched green energy scheme.

DUP MP Sir Jeffrey Donaldson insisted there was no appetite within his party to pull down the institutions in the way the late Martin McGuinness did when he quit as a joint head of government in January 2017.

He said the Northern Ireland public should not be deprived of a government during the pandemic.

“The First Minister has provided strong leadership to Northern Ireland and I don’t see why the answer to this is to deprive the people of Northern Ireland of a government when they need government, effective government most in the middle of this pandemic,” he said.

Sir Jeffrey added: “We will act responsibly, we will provide leadership. We want to see Sinn Fein step up to the mark and I hope that they will do the right thing. But I don’t see why the First Minister should resign when she is not in the wrong here. Arlene has abided by the rules, she has set a clear example, it is a matter of regret that the Deputy First Minister couldn’t do the same.”

On Wednesday, Mrs Foster urged Ms O’Neill to apologise and make amends for what happened at Tuesday’s funeral in west Belfast.

The Deputy First Minister declined and defended her actions, insisting she acted within Covid-19 rules and guidance.

She differentiated between the management of the funeral cortege and service and scenes along the route when hundreds gathered to watch the procession pass. Ms O’Neill insisted that was outside of her control.

The DUP called for Ms O’Neill to step down following her refusal to apologise.

Sir Jeffrey said the executive’s public health message had been damaged.

He said it would not be “business as usual” at Stormont until the row was resolved, suggesting Mrs Foster would not be appearing alongside Ms O’Neill for future joint media briefings on the Covid-19 emergency.

“She should step back from her duties in the meantime to help immediately rebuild confidence with the public so that we can have a clear message from the executive that the public don’t see double standards on the part of ministers and that’s vital,” he said.

Updated Stormont lockdown measures currently limit funerals to a maximum of 30 people – having previously been 10.

Friends should only attend when there are no family members of the deceased in attendance, according to the rules and guidance.

The Diocese of Down and Connor has said St Agnes’ Church should still have been applying the 10-person limit to funerals on Tuesday morning.

The diocese said it was only informed by Stormont officials on Tuesday evening that more numbers could be accommodated.

It is understood that more than 100 people were inside St Agnes’ for Mr Storey’s funeral.

While Stormont is anticipated to sign off guidance that would allow more people to attend a funeral, depending on the size of the church, that move has not yet been announced.

Police have said they are investigating whether there were any breaches of lockdown rules during Tuesday’s events.

Ms O’Neill has insisted the funeral cortege was limited to 30, while social distancing inside the church was “exemplary”.

However, she has acknowledged that a selfie taken at the cemetery of her posing close to two men, one of whom had his arm on her shoulder, “should not have happened”.

She said the photo happened in a “blink of an eye” as she was leaving the graveside.

Also on Thursday, the SDLP called for Ms O’Neill to step aside and allow her actions to be examined by Assembly standards authorities.

SDLP deputy leader and Stormont infrastructure minister Nichola Mallon said: “We always have to show leadership even in the midst of our grief and a lot of hurt has been caused, and I think an apology earlier on would have helped this situation.”

The Ulster Unionist Party and Alliance Party have also called for Ms O’Neill to stand down.

There was one further coronavirus-linked death reported in Northern Ireland on Thursday, taking the total recorded by the Department of Health to 552.

There were seven new cases of the virus confirmed, bringing the total in the region to 5,768.