A number of parades have since been prevented from going beyond the Woodvale Road junction.
At the weekly protest on Saturday afternoon, supporters were told by Portadown District Master Darryl Hewitt that the Parades Commission is not fit for purpose.
"We have said on numerous occasions that the non-Parades Commission is not fit for purpose and that it should be changed, not only in terms of the personnel but more importantly changes must be made to the flawed legislation that brought it into being," Mr Hewitt said.
"It seems to be that once the republican community threaten violence then it is us that have our civil and religious liberties denied."
He continued, saying: "As I am sure you are aware our Grand Master issued an invitation to Dr Richard Haass to visit both Portadown and Twaddell Avenue to learn at first-hand what the real problems are.
"I am sure that you would join me in supporting wholeheartedly the Grand Master's invitation by declaring today that none of us will be found wanting if we get the opportunity to meet with Dr Haass."
Dr Haass is the independent chair of all-party talks on flags, parades and other unresolved issues in the region.