Published Tuesday, 03 September 2013
It comes after a compromise was reached on a Sinn Féin motion on Monday night.
The party had put forward a proposal condemning an attack on Mr Ó Muilleoir at a park in north Belfast, and supporting his right to carry out civic duties in any part of the city. Police had to shield the Lord Mayor when he was swarmed by loyalist protestors last month.
The DUP did not support the motion - but at the last minute, following a round of talks, Sinn Féin withdrew it and entered an alternative motion which was backed by all the parties.
It refers to all the violence of the summer and contains a commitment to show leadership.
A potential political row was averted with the passing of Monday night's vote.
The DUP had said it would not support the original Sinn Féin motion, which focused on events at Woodvale Park in the Shankill area on 6 August, as it was too narrow.
An agreement was reached to amend the proposal.
Describing the situation on the streets in north Belfast as "very tense", DUP councillor Lee Reynolds said: "It's been progress that we've came together with an agreement."
Alliance Belfast Councillor Tom Ekin welcomed the unanimous support for the motion.
"Following a difficult summer, there was a tremendous feeling that there was a need for Belfast Council to show leadership. The decision by the political parties to unanimously support this motion has shown that we can be progressive instead of regressive."
He added: "We are beginning to show the political leadership in Belfast that the public deserves. Belfast Council has delivered a positive message to the City and beyond by agreeing to this motion."
Cllr Ekin continued, saying that all councillors must be expected to maintain and strengthen the civic responsibilities of this Council.
"It is vitally important that this is demonstrated at all times by every Councillor."
Cllr Ó Muilleoir met with his Dublin counterpart Oisin Quinn at City Hall on Tuesday, and revealed plans to meet London Mayor Boris Johnston in the next two weeks.
He said Belfast is a "city transformed" and added that progress must be continued by building links and sharing learning with other big cities.
The Lord Mayor continued: "In recent years, Belfast has been transformed and this is reflected in the fact that tourist visitors to the city continues to grow, with the south of Ireland and Great Britain being important markets for us."
"Working together to attract tourists and investment to our island and exploring other mutually beneficial initiatives is positive and a sensible course of action and I look forward to exploring similar opportunities with the Lord Mayor of London when I meet him next week."
© UTV News