Chief Constable Simon Byrne has said "widespread violence and disorder" would have followed any attempt to disperse large crowds attending the funeral of senior IRA figure Bobby Storey.
Mr Byrne defended how it was handled and said the investigation into potential breaches of health regulations was "in its end stages".
He also acknowledged "hurt" had been caused by the policing of Black Lives Matter protests.
However Mr Byrne declined to apologise.
There have been lingering criticisms of how the Police Service of Northern Ireland (PSNI) dealt with the events, which occurred in June amid curbs on large gatherings.
Last month, a report by the Policing Board found police actions at the Black Lives Matter demonstrations in Belfast and Londonderry may have been unlawful in preventing legitimate protest.
In an interview with BBC News NI, Mr Byrne said he was not prepared to apologise at this stage.
Referring to a continuing Police Ombudsman investigation, he said: "If in the fullness of time we have got things wrong I will come out and say so.
"The time to do apologies is when we have got the total picture."
He has announced a new community relations task force, which will work to build a better bond with ethnic minorities.
About 1,800 people attended Mr Storey's funeral in west Belfast.
Police largely stayed away, leaving Sinn Féin stewards in charge of mourners, who included several of its ministers in the Northern Ireland Executive.
Deputy First Minister Michelle O'Neill, one of 24 people under investigation, later admitted the public health message had been undermined.
Mr Byrne said the PSNI had not abdicated its responsibilities.
"We are in nobody's pocket, we do not collude with anybody, we just have to use discretion which is at the heart of our policing style."
He said it was "not appropriate" to comment on what the police and Sinn Féin had discussed in advance of the funeral.
Sinn Féin president Mary Lou McDonald had previously said it had been "meticulously" planned with the PSNI.
Acknowledging there was no review or investigation into police actions that he was aware of, Mr Byrne said: "I am limited about what I can say at the moment.
"I do not want to be drawn about who said what, to who and when, just at this point in time.
"It is absolutely right to ask the question, but it would be best answered in a few weeks."
Threat of violence
Meanwhile, the Sinn Féin's Gerry Kelly said it was "ludicrous" to suggest that widespread violence would have followed any police action to disperse mourners at the funeral.
The North Belfast assembly member said remarks by Mr Byrne had caused hurt to Mr Storey's family.
Both the DUP and Ulster Unionists have said Mr Byrne must reveal more about what discussions police had with Sinn Féin in advance of June's funeral,
"You just do get a sense that they're pandering towards Sinn Féin in some way," Ulster Unionist assembly member Doug Beattie said.
"This business that if it was broken up there'd be a threat of violence - the threat of violence from who? From the people, organised violence? Spontaneous violence?"
DUP MP Carla Lockhart said: "The chief constable has openly admitted that the threat of public violence and disorder dictated the policing response to the Storey funeral.
"It is humiliating that the enforcers of law and order in Northern Ireland should bow to such a threat."
This story was amended on 28 January 2021 to remove the phrase 'IRA veteran'