The DUP has supported deputy lord mayor Ruth Patterson after she snubbed the newly elected Sinn Fein lord mayor at a Belfast council meeting on Thursday.
Sinn Fein's Niall O Donnghaile, 25, offered his congratulations to Mrs Patterson but she did not acknowledge him.
"I wanted to wish her congratulations, it is unfortunate she refused to accept them," Mr O Donnghaile said.
Mrs Patterson was not available, but in a statement, her party backed her.
Alderman Robin Newton, DUP group leader on the council, said his party was committed to a positive agenda in Belfast.
"Ruth Patterson has been a Councillor for more than ten years. She knows how Council meetings should be conducted and what the protocol is for such occasions.
"She will be a fine ambassador for our city and brings a wealth of experience and dynamism to the role which others can only aspire to," the statement said.
Mr Newton referred to the recent rule change in how top council positions are allocated. Positions such as lord mayor and deputy lord mayor will now be handed out on the basis of party strength and not that of political groupings.
Mr Newton said his party would "not shy away from calling out anti-unionist discrimination".
He added: "For every year there is a Sinn Fein lord mayor, there will be a DUP deputy lord mayor: to ensure inclusion and fairness in the city hall."
Speaking earlier on Friday, on BBC NI's Good Morning Ulster, Mr O Donnghaile said: "I intend to work with all of the council members and that includes the deputy mayor and her fellow members of the DUP."
He said he felt privileged to be offered the position, despite having been a councillor for just three weeks.
"Sinn Fein are willing to put younger political activists forward for leadership roles and I am very proud to be put forward by the party," he said.
"Many young people in our city do feel overlooked, left out and lost. The onus is not just on the council but on us as people within Belfast to give them a voice."
The new lord mayor said he intended to represent all of the people of the city.
"I do want to be a mayor for all ... not just unionists, loyalists, but republicans and nationalists and many different people who make up our city.
"I am confident that we can move the city forward in this new term."