On Tuesday the Sinn Féin representative was forced to flee the ceremony at a children's playpark in Woodvale Park in the Shankill area after he was mobbed by an angry crowd.
He was checked in hospital and was said to be "sore" afterwards. Nine police officers were also injured as they led the city's first citizen to safety.
It had emerged on Tuesday that the DUP had written to the Lord Mayor warning him not to go to the Woodvale area for the event.
Reacting on Wednesday, Mr Ó Muilleoir said he always considered advice from the PSNI as regards to safety at events.
"The first thing we should commend the police officers who were attacked yesterday," he said.
"My schedule will be set by the officers, by those who invite me and on the advice, always, of the PSNI.
"So there may be some elements within the DUP who wish to set my schedule for me but I'm not going to accept that."
The mayor said he has been contacted by politicians from different parties since the incident.
"I think people are revulsed by this but they believe in Belfast like I do. We're going to continue to push Belfast on. We come from a very dark place, a dark past," he continued.
"There's a small violent element who attacked the police, they did it on the Twelfth of July, they did it yesterday - they want to attack the first citizen.
"My message to the people of Belfast is don't be distracted, don't be deflected. I said I'd represent everybody in the city, I said I'd visit every part of the city. We're going to proceed cautiously. We want to build the peace and I'm convinced that I have the good wishes of the vast majority of Belfast."
I have been telling everyone in this city that I represent all the people in the city and I'm going to continue to do that.
Máirtín Ó Muilleoir, Belfast Lord Mayor
DUP councillor Brian Kingston condemned the attack on Wednesday.
"That violence is wrong," Mr Kingston commented.
"I do not condone violence. It should not have happened. And it takes away from whatever message people are trying to make by having a protest - that is always the case.
"I'm aware that the Lord Mayor was injured, police officers were injured and some of the protestors were injured. That happened when the police formed this tight cordon and forced their way through the protesting crowd in order to get the Lord Mayor safely out of the location."
He added: "But all of that takes away from people's legitimate protests and legitimate grievances."
Meanwhile Sinn Féin's group leader in Belfast, Cllr Jim McVeigh has called for the DUP to bring all their members into line with party policy, claiming that William Humphrey, the former DUP group leader on the council, had refused to talk to their party.
Mr Humphrey had said on Tuesday that the protest was a response to Mr Ó Muilleoir's part in Sinn Féin supporting the restricting of the Union flag at Belfast City Hall back in November.
"It seems that Cllr. Humphrey, who also double jobs as an Assembly member, has missed the point that his party leader jointly leads the Executive alongside Martin McGuinness. He seems locked in a pre-peace process time warp," Cllr McVeigh commented.
"It is the sort of mindset that prevents him from condemning attacks like the one yesterday on the Mayor or tries to explain away the placing of religious statues on loyalist bonfires over the Twelfth.
"The DUP have many good and decent members in Belfast City Hall who want to engage and want work collectively for the betterment of Belfast. They are being held back by the sectarian and backward behaviour of a few."
PSNI North Belfast Area Commander Chief Inspector Andy Freeburn has branded Tuesday's event as "appalling" and has said officers will be investigating with a view to identifying those responsible.