The DUP lodged the request on Wednesday, which leader Peter Robinson said will "allow for the expression of opposition to a decision which many see as rewarding riotous behaviour by dissident republicans last July".
On UTV Live, Chairman of the Parades Commission Peter Osborne denied that the body was rewarding the threat of violence.
"That is just not true - and I think anybody who says that probably hasn't read the determination," he said.
The determination that we issued has at its core the need for dialogue, the need to resolve community tension and improve community relations.
Peter Osborne, Parades Commission
The First Minister had insisted that a Stormont debate would "provide the opportunity to examine why it is that some feel the need to oppose the sharing of roads and to support tactics which ultimately disregard respect for the culture of those from the unionist community".
Mr Robinson added that Parades Commission decisions "do nothing to encourage mutual respect and tolerance for culture and identity" and that "recent outcomes have served to divide and polarise the wider community".
He said that progress involving dialogue between lodges and residents had not been recognised.
"The DUP is committed to building a shared future in Northern Ireland, but that must be a shared future which includes members of the Loyal Orders and bandsmen across the province," Mr Robinson said.
"If that is not the case, then it is not a shared future we can support."
The DUP leader appealed to all concerned to "use every possible influence over the next few days to ensure a peaceful and dignified Twelfth".
Continued refusal to tolerate the passing of a short parade fuels the view that nationalists and republicans have little interest in building a genuinely respectful and tolerant society.
First Minister Peter Robinson
The Orange Order has described the restriction preventing Friday's return parade as "ludicrous".
In a statement, the Order said that the ruling had "effectively signed the death warrant of this discredited and unaccountable quango".
The Order added that the County Grand Orange Lodge of Belfast had made "genuine and sincere efforts to diffuse tensions on parades in the area".
"Ligoniel brethren took the bold and proactive decision to engage with nationalist residents following on from the publication of the comprehensive template, designed to address the issue of respect concerning St Patrick's Roman Catholic Church," the statement said.
"Despite such unprecedented initiatives, the Parades Commission has opted to reward violence and notably the threat posed by dissident republicans."
The County Orange Lodge of Ireland advised supporters not to be drawn into violence and said it "looks forward to a peaceful day" on Friday.
This antiquated and unelected body is clearly not content in merely stifling our proud Protestant culture and heritage, but increasingly by its actions, is causing irreparable damage to community relations and a so-called shared future in north Belfast.
Earlier, the Greater Ardoyne Residents' Collective (GARC) called off a protest march in the area on the afternoon of the Twelfth following the watchdog's ruling.
The group still plans to stage a morning protest.
On Tuesday, prior to the ruling, around 50 members held a white line protest in opposition to the parade - which they argue causes major disruption and inconvenience to the community in the area.
On Wednesday night Sinn Féin North Belfast MLA Gerry Kelly said that Crumlin Ardoyne Residents' Association (CARA) had also decided to call off a protest on Friday morning.
Welcoming the news, he said: "I attended a public meeting tonight organised by CARA where they gave an update to the residents of Ardoyne on the talks with the Orange Order and had the support of the hall to reengage with the Orange Order as soon as possible after the 12 of July.
"CARA's position was well received by those who attended the meeting and the residents of Ardoyne are hopeful of a peaceful 12 of July."
He said that dialogue should now continue.
Friday morning's Orange parade will go ahead in the Ardoyne area with no music or drumbeats and only 100 supporters allowed to accompany the lodges and bands.
On their evening return parade, Orangemen and bandsmen will be stopped at the junction of Woodvale Road and Woodvale Parade.
The constant pressure by GARC and the community of Ardoyne has forced the Parades Commission to capitulate from their position of facilitating unwanted outdated provocative acts of sectarian triumphalism.
UUP councillor Mark Cosgrove, a member of the Belfast Parades Forum, hit out at the ruling.
"Last year's events at Ardoyne proved beyond any doubt that there was absolutely no connection whatsoever between the Orange Institution, who complied fully with the restrictive determination to parade home at 4pm, and the subsequent mob rule that took to the streets in the name of protest several hours later," he said.
"The arrogance of the Commission in suggesting after last year's events that, if the Orange Order do what they are told in the coming weeks and months, that they will look favourably on an evening return parade next year is as perverse as it is lacking in simple natural justice."
But SDLP North Belfast MLA Alban Maginness said: "This decision by the Parades Commission to stop the return leg of the parade on the evening of the Twelfth of July has created the space for GARC to cancel their planned protest, which will hopefully further reduce tensions.
"This was a common sense decision and should be acknowledged as a positive contribution to creating a peaceful Twelfth in Ardoyne."
That decision to begin the talks was a brave one by both the residents’ group CARA and the Orange Order.
Gerry Kelly, Sinn Féin
Alliance North Belfast spokesman John Blair said the Parade Commission ruling must be upheld.
"It is essential that elected representatives ensure their words and actions over the next few days leave no room for those who might take advantage of heightened tensions to see them as an endorsement of law-breaking," he added.
The Parades Commission issued its unprecedented determination in the absence of agreement between the Orange Order and local nationalist residents.
The annual feeder parade in the area has been marred by serious violence in recent years and it was hoped talks could pave the way for a more peaceful Twelfth this year.
The face-to-face talks, held at the weekend, were initiated at the request of a loyalist residents' group, the Twaddell and Woodvale Residents Association, who called on three local lodges in north Belfast to engage in direct dialogue with CARA.
On Tuesday evening, the Parades Commission said it was "disappointed" that the Orange Order did not engage directly with CARA until six days before the parade.
However, they did welcome the commitment from the two sides to continue talks in the future.