A Portadown Orange Lodge spokesman has denied the movement was divided over tactics.
"Our resolve now to walk the Garvaghy Road is as strong as it ever has been. We wouldn't have that resolve if we didn't think that was possible," Mr David Jones told BBC Radio Ulster.
He criticised the stance of Garvaghy Road residents opposed to the march and defended the order's insistence on dealing with them only through mediation.
"We haven't spoken directly to the Garvaghy Road residents because quite simply during all the proximity talks in which we were involved there has never been any sign or any movement to make that at all possible," he said.
"Whenever we ask the Garvaghy Road residents - and you can see it in the review of the Parades Commission determination - what is the problem with the parade, they have never come up with a legitimate answer.
"They talk about many issues which unfortunately the Orange Order can't have direct input into," the spokesman said.
RUC Chief Constable Sir Ronnie Flanagan today welcomed the relative state of calm, which he attributed to a variety of factors "not least among which is the very responsible attitude taken by the Orange Order".
He said: "Whatever is the intended way forward, whatever is the means of bringing about a solution, one things is absolutely certain: force of numbers, violence, is counter-productive.
"I think people realise that, I think people distance themselves from it and the calls that were made yesterday [for peaceful protest at Drumcree] were very helpful and the way the Orange Order behaved last weekend [at a parade across the west Belfast peaceline] was very helpful."
PA