Sinn Féin deputy first minister Martin McGuinness and Democratic Unionist Party deputy leader Arlene Foster clashed at the North South Ministerial Council meeting over the flying of the Irish Tricolour on Stormont House.
Mr McGuiness dismissed the controversy as "much ado about nothing" and said unionists were "over-reacting" about the incident.
However, Ms Foster insisted it caused "huge offence" and called on the authorities to "get to the bottom" of how it happened as soon as possible.
The Police Service of Northern Ireland launched an investigation after the Irish flag was flown over the parliament building in Northern Ireland on Wednesday.
The hugely divisive issue of flags and parades has led to violent clashes between protesters and police in recent years.
Mr McGuinness and Ms Foster were speaking alongside Taoiseach Enda Kenny, Tánaiste Joan Burton and Foreign Affairs Minister Charlie Flanagan at the North South Ministerial Council meeting
There was wide-ranging discussions between leaders north and south of the border on issues including fuel smuggling, the all-Ireland bid for the Rugby World Cup and the ongoing tensions over the Northern Assembly's welfare budget.
Mr McGuinness condemned the criminals involved in fuel smuggling - and said they were damaging the peace process.
Mr Kenny committed to raising the issue of Northern Ireland welfare cuts at his meeting with British Prime Minister David Cameron in Downing Street on June 18. The Northern Ireland Assembly is at crisis point over its budget.
Mr McGuinness and Mr Kenny said they were both in favour of a cross-border investigation into allegations of republican sex abuse.
Authorities in both jurisdictions are carrying out separate investigations into allegations that sex abusers were moved both north and south of the border by the IRA.