Sinn Féin will co-operate with the Police Service of Northern Ireland (PSNI) over any potential investigation into the protest on the Garvaghy Road, the party president has said.
Protesters have remained on the Garvaghy Road since Sunday 27 September as the fallout over the proposed Portadown District Orange Lodge march continues, and rallies on both sides of the dispute were held on Saturday.
Mary Lou McDonald has said that "there's no question with us co-operating with any process that will unfold".
Speaking on Sunday, Portadown District Master Nigel Dawson said police confirmed to them that Saturday's gathering on the Garvaghy Road was "unnotified" and police were "taking evidence".
McDonald and Northern Ireland's First Minister Michelle O'Neill are among those who have attended the protest, which police have described as unnotified and "therefore illegal".
The Portadown District has maintained a presence at Drumcree Church after talks to end the parading dispute ended without agreement on Thursday.
The Portadown District attempted to march again on Sunday morning.
The PSNI said that anyone "found to have broken the law will face criminal justice consequences".
However, speaking on the BBC's Sunday Politics programme, McDonald said: "There are moments in politically life where you have to take a stand, and this is one of those moments."
When asked about the legality of the protest she said: "Others will determine whether or not that is in fact the case."
The Parades Commission's decided that the parade - which is opposed by residents of the Garvaghy Road - could go ahead on Sunday 27 September with restrictions.
A fresh legal bid by the residents to prevent the march was due to be heard on Friday - but has now been postponed until Monday.
Speaking of how many times the Portadown District have attempted to proceed with their march in the past week, Dawson told BBC News NI on Sunday: "I haven't been keeping a running check on it, but I think it's 15 times we have attempted to implement the determination issued by the Parades Commission and re-enforced by a High Court judge."
He said that "on each and every occasion the message from the PSNI headquarters is they are unable to offer us safe passage down the road".
"So we continue to be here waiting for the Chief Constable to apply the law to a lawful determination," Dawson said.
"Obviously I'm not involved in policing matters and we respect the police but I suspect that time is running out, that he can't continue to say that he is unable to his job."
Dawson said Portadown remains a "very determined district".
"Some of us have been here for the last 28 years each and every Sunday, and we are happy to allow the law to take its course but the law needs to be implemented and it needs to be respected by everybody across the communities."
The actions of McDonald, O'Neill and others have received condemnation including from members of the Democratic Unionist Party (DUP).
In a post on social media, deputy First Minister Emma Little-Pengelly said the "behaviour of Michelle O'Neill and her party has been disgraceful" and a "complete abdication of leadership".
McDonald said that this "comes down to right and wrong", and that as people who care passionately about the future, her and O'Neill know that for "that to happen we have to stand four square with the community of the Garvaghy Road".
She said there was a "broad crowd politically and otherwise" at the rally on Saturday, adding that it was "resolute but good humoured with a real eye for the future".
"I cannot fathom anybody suggesting that 28 years on when progress has been made in such significant ways, not least in Portadown and in the wider Garvaghy community, why it is that anybody would seek to reopen that wound."
Meanwhile, in response to DUP leader Gavin Robinson's comments that Sinn Féin is attempting to goad unionists into collapsing Stormont, McDonald said it is "anything but", adding that it is about the ability of communities to live work, and build futures together.
Drumcree was one of Northern Ireland's most serious parading disputes, when stand-offs over attempts by the Orange Order to march along the Garvaghy Road were accompanied by riots, roadblocks and killings.
When the Orange Order was prevented by police from walking down the route in July 1995, there was a tense stand-off. It was the same for the next three years.
In 1998, the newly-established Parades Commission ruled that the Orange Order should not march down the road - a decision that was upheld for the past 28 years.
The row re-emerged last month after a court case in which a ruling by the Parades Commission was overturned, and a fresh application to parade was lodged.
Last Friday, the commission decided that the march could go ahead with restrictions in place.
However, that decision was challenged in several Belfast courts on Saturday, before finally being given the go-ahead just hours before it was due to take place.
