Mr Muir was speaking after Belfast Lord Mayor Máirtín Ó Muilleoir was jostled and heckled as he attempted to attend the re-opening of a park in North Belfast. Nine Police officers were injured during the incident.
Mayor Muir said: “I completely condemn this shocking incident and would call on other political representatives to join me in my condemnation.
“As the Mayor of North Down I represent everyone across the borough and have enjoyed welcoming groups to the Town Hall from all backgrounds and sectors and attending a diverse range of events.
“Together, working as one, we are building a stronger shared future for North Down, with inclusiveness among my top priorities. Having delivered this message across North Down I would expect my Belfast counterpart to have the same freedom to travel across Belfast, as he aims to represent all sides of the community.
“We cannot allow tribal politics to continue dominating the agenda in Northern Ireland. It is disappointing that not only was the Lord Mayor’s safety put at risk, but nine PSNI officers were injured protecting him.”