DUP leader Gavin Robinson has announced the party’s deputy First Minister Emma Little-Pengelly is to cease participating in joint engagements with Sinn Féin First Minister Michelle O’Neill.

Mr Robinson said Ms Little-Pengelly will also not be giving permission for Ms O’Neill to fulfil engagements on her own in the role of First Minister.

His announcement came after DUP party officers convened on Thursday to discuss how they should respond to Ms O’Neill and several of her party colleagues being investigated by police for participating in an allegedly unlawful protest on the Garvaghy Road in Portadown last month.

The protest was staged as part of efforts to prevent a contentious Orange Order parade proceeding down the predominantly nationalist road from nearby Drumcree Church.

Ms O’Neill, who last week attended a police station for interview, has defended her presence at the protest as the “right thing to do”.

While stopping short of withdrawing Ms Little-Pengelly from her post – a move that would also force Ms O’Neill from her role and collapse the Stormont Executive – Mr Robinson told reporters on Thursday he could not give an assurance he would not ultimately take that step.

“Michelle O’Neill’s arrogance will have consequences for her,” he said.

The practical outworking of the move means Ms O’Neill and Ms Little-Pengelly will not attend an economic event in Glasgow on Friday.

Stormont’s leaders were scheduled to meet with Prime Minister Andy Burnham, Scottish First Minister John Swinney and Welsh First Minister Rhun ap Iorwerth.

Ms O’Neill and Ms Little-Pengelly were also due to hold a separate meeting with Mr Burnham in Glasgow to discuss the ongoing impasse over the lack of Stormont budget for the current financial year.

Posting on social media before Mr Robinson officially announced his party’s decision, Ms O’Neill claimed blocking participation in the Glasgow conference was a “reactive stunt, driven by the DUP’s own internal pressures and electoral problems”.

She added: “The Economic Forum is taking place tomorrow in Glasgow, and this reckless and irresponsible approach of Emma Little-Pengelly means the people of the north will not be represented.”

Mr Robinson said his party’s blockade also means an already-postponed meeting between Ms O’Neill and Ms Little-Pengelly and Irish President Catherine Connolly at her official residence at Áras an Uachtaráin in Dublin will not now take place.

Withdrawing Ms Little-Pengelly from her post would automatically force Ms O’Neill from office due to the joint nature of the powersharing structures in Northern Ireland.

Such a step would effectively collapse the devolved administration in Belfast as the Executive could no longer meet to make significant decisions.

However, individual departmental ministers would remain in post for up to six months and the Northern Ireland Assembly could continue to sit.

Mr Robinson has faced calls from some within his party, most notably Upper Bann MP Carla Lockhart, to pull out the deputy First Minister.

He has argued that such a move would be bad for unionism and also punish people across Northern Ireland – as the administration could no longer take decisions on key issues.

“The First Minister needs to be held accountable for her actions and for her recklessness,” he told reporters at Stormont.

“We believe that while she and her colleagues should be punished, that does not include punishing the rest of Northern Ireland, the foundation of democratic principles that hold society together.

“There has to be accountability, but not at the expense of public sector pay or a budget that is there to provide basic and decent public services for the rest of the people of Northern Ireland.”

The furore is playing out amid the customary political manoeuvring that takes place at Stormont ahead of an Assembly election. The next poll is currently due to be held in May.

A decision by the Parades Commission adjudication body to allow the Orange Order to parade down the Garvaghy Road for the first time in almost 30 years prompted a two-week stand-off at the site of what was a notorious parading flashpoint during the Troubles.

The parade was ultimately unable to take place because of significant numbers of protesters on the Garvaghy Road, leading Northern Ireland Secretary Sir Chris Bryant to overturn the commission’s decision and ban the procession. His decision was upheld by a High Court judge on Wednesday.

Under parading laws in Northern Ireland, protests must be notified to, and approved by, the Parades Commission.

Police investigating the unnotified Garvaghy Road protest, which was staged on the day the Drumcree parade was meant to proceed on September 27, have said invitations to attend interviews were sent to individuals “reasonably suspected of committing offences”.

Sinn Féin TDs Pearse Doherty and Matt Carthy were the latest party representatives to attend for voluntary interview with the police in Belfast on Thursday.

Arriving at Musgrave Street in the city centre, Mr Doherty said he and his party were “proud to have stood with the Garvaghy Road community and defended 28 years of peace”.

“Standing up for what is right is always the right thing to do,” he said.

“We believe that it is right to have taken this stand and supported the peace process, supported the progress that we have seen.

“We defend the progress that we have seen over the last number of years, and there is no going back.”

Mr Carthy added: “Just to reiterate, myself and Pearse and other Sinn Féin representatives will be attending voluntarily for an interview with the PSNI.

“The interview will relate to the peaceful protest that we attended on the Garvaghy Road, and our view very strongly is that the parade on the Garvaghy Road was not a tolerable prospect, and that the peace that has been built on very painstakingly over the past 30 years is something to be protected.”