Unionists have been angered by the hanging of the Tricolour in the office of Belfast's Sinn Féin Lord Mayor.
Mr Alex Maskey said that placing the Tricolour alongside the Union flag, which is already in his parlour, would be a move towards equality.
However, unionists have said that the flag of a "foreign country" should have no place at Belfast City Hall. The Tricolour was presented to Mr Maskey by a former Provisional IRA prisoner at a ceremony yesterday.
Photographs of Queen Elizabeth, Prince Phillip and the late Queen Mother are already on the walls. The Tricolour stands on one side of the ornate fireplace in the Lord Mayor's parlour and the Union flag is on the other.
Mr Maskey said that he had made a "solemn promise" not to remove the Union flag from his office. The council should consider flying both flags together on the roof of City Hall.
"If the Union flag is there, the Irish flag should be there alongside it.
"If we have equality of flag-flying, fine. If we have neutrality of flag-flying and no flags, I am happy with that also."
Mr Maskey suggested that there could be a civic flag to which all traditions could give allegiance.
He said that he did not intend to offend unionists.
"During my term of office, I want the word 'equality' to shine like a beacon through everything I do."
Ulster Unionist Mr Jim Rodgers, a former lord mayor of the city, said that Belfast was part of Northern Ireland and the flag was the Union flag. No other flag should be flown.
A former DUP lord mayor, Mr Nigel Dodds, said that the installation of the Tricolour contradicted Mr Maskey's claim that he would "represent the people of this capital city, part of the UK, in a fair and non-controversial way".