The Rev Mervyn Gibson, Orange Order Chaplain, echoed Drew Nelson's apology after visiting the priest at St Matthew's to apologise for the bandsman's behaviour.

"I would fully support that apology, indeed as a local Minister and neighbouring Minister and as a member of the Grand Orange Lodge I visited Fr Aidan Keenan this morning and spoke with him and told him we would be sending out a letter of apology to him with what happened with the bandsman's actions, there is no excuse for it whatsoever," Rev Gibson told UTV.

Tens of thousands of Orange members and supporters took part in the parade through Belfast - one of the biggest ever organised in Northern Ireland - to mark the 100th anniversary of the 1912 proclamation against plans for Home Rule in Ireland.

Marchers were ordered to play only sacred when passing St Matthew's on the Newtownards Road and near St Patrick's Church on Donegall Street.

Meanwhile a protest held by the Carrick Hill residents' group in north Belfast was limited to 150 participants.

There were large signs at locations to remind bands and protestors of the restrictions in place.

I think the decisions the Commission took for this parade were absolutely right. I think it is entirely appropriate at sensitive locations at interfaces that sacred music or hymn tunes are played.

Parades Commission Chair Peter Osborne

Police praised the efforts which allowed the day to pass off "in relative peace and calm" but nationalist politicians have said that some bands had behaved provocatively near the two Catholic churches, with claims the Sash was heard being played on the day.

The Orange Order said some bands may have played exuberantly, adding the Parades Commission determinations were too stringent, especially in north Belfast.

"The length during which the Parades Commission imposed those restrictions were much longer than just the front and the immediate area around the church," Drew Nelson said.

On Monday, Parades Commission Chair Peter Osborne said parade organisers would have to look at behaviour in some instances of potential breaches.

He stressed the fact that the parade "passed off largely peacefully is positive". He also called on the Orange Order to take the next step and meet with residents.

"The last two or three weeks have seen an improvement in that context, there has been some dialogue, if not as much as there could be, engagement by civic leaders and senior politicians and clergy has been really important," he told UTV.

"The work for next year needs to start now," he added.

But Sinn Féin MP Conor Murphy has said the events leading up to and during the parade exposed what he called the "nonsense of the argument" that unionism was an ideology that could attract support from across the community.

Mr Murphy said: "Saturday was about supremacy, it was about intolerance and it was about triumphalism. The rights of nationalist residents in Carrickhill and the Short Strand were secondary to a unionist demand to march past Catholic Churches whilst playing sectarian tunes."

Sinn Féin has called on First Minister Peter Robinson to condemn bands that allegedly breached the Parades Commission ruling.

Police say evidence was gathered extensively throughout the day and any breaches of the Parades Commission ruling will be investigated and reported to the Public Prosecution Service.

Police say they are also investigating an attack on Clifton Street Orange Hall, from where Saturday's parade started. Paint bombs were thrown at the building in the early hours of Monday morning.