First Minister Arlene Foster has said police must show that no one is above the law.
Mrs Foster made the comments after a meeting with PSNI Chief Constable Simon Byrne over potential breaches of coronavirus regulations at the funeral of senior republican Bobby Storey.
Deputy First Minister Michelle O’Neill and Finance Minister Conor Murphy were among hundreds who attended the funeral.
On Tuesday evening, the Stormont Assembly passed a motion urging Ms O’Neill to apologise for attending the funeral amid the pandemic.
The resolution was backed by the DUP, UUP, SDLP and Alliance – but does not have any practical legal effect.
Ms O’Neill has apologised “for grieving families experiencing more hurt”.
Mrs Foster has asked her powersharing partner to step aside while PSNI officers consider the matter.
The DUP leader had a virtual meeting with Mr Byrne on Wednesday morning.
Speaking afterwards, she said: “It is vital that the police send out a clear signal in all their actions that no one is above the law.
“There can be no special status as far as the law is concerned. We are all equal under the law and equally subject to it.
“The Chief Constable has a duty to fully investigate all alleged breaches and demonstrate to the public that the rules are being implemented fairly.”
Fundamental to a society based on law and order is that we are all equal under the lawMervyn Storey
DUP MLA Mervyn Storey added: “There are very significant questions for the police to answer as to what engagement they had with the organisers of the Bobby Storey funeral and the nature of that engagement.
“There are many law-abiding citizens deeply angered and concerned that the policing of this funeral seems to have taken a different approach to other mass gatherings.
“Fundamental to a society based on law and order is that we are all equal under the law.
“Today’s meeting was an opportunity to remind the Chief Constable that irreparable damage would be done to the reputation of the police if this investigation was not seen to be handled in a manner which is beyond reproach.”