Hundreds of people packed into a hall near the Garvaghy Road to be told about the outcome of earlier talks, as the stand-off in Portadown entered its third day.
The media were not given access to the meeting.
Speaking after the meeting, Breandán Mac Cionnaith of the Garvaghy Road Residents' Coalition said he wanted a meeting with the PSNI's Chief Constable.
Mr Mac Cionnaith said Jon Boutcher should "stop hiding" and come and meet the people directly affected by the planned parade.
He said the vast majority of the residents did not want the parade to go ahead and that the Northern Secretary had been left in no doubt about that.
Earlier, Taoiseach Micheál Martin and Minister for Foreign Affairs supported the idea of an independent international figure playing a role as a mediator.
Ms McEntee said she believed it was "likely" an international mediator would be appointed to attempt to intervene.
Northern Ireland Secretary Chris Bryant, meanwhile, called for all sides to "double down on compromise" to find a resolution to the Drumcree parading stalemate.
Speaking after a meeting with Mr Bryant that he called "very positive and constructive", Orange Order Portadown District Master Nigel Dawson said "we look forward to the law being applied to the parade".
Members of the Garvaghy Road Residents' Coalition also met with Mr Bryant at Hillsborough Castle.
Mr MacCionnaith said it was "debateable" whether any progress had been made on the impasse.
Northern Correspondent Conor Macauley with latest from Garvaghy Road
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Stormont First Minister Michelle O'Neill said both the Taoiseach and Tánaiste Simon Harris had given assurances to use their offices to engage with the British government in relation to the ongoing situation, after meeting the duo alongside her party leader Mary Lou McDonald at Government Buildings this evening.
The Sinn Féin leadership had sought for Mr Martin and Mr Harris to urgently intervene in the dispute and ask Mr Bryant to use his legal powers to stop the Orange Order parade along the Garvaghy Road.
Ms McDonald had earlier accused Northern Ireland Secretary Chris Bryant of "sitting on his hands" over the dispute.
Mr Bryant was due to meet Ms McEntee in Belfast tonight.
A number of Orange Order members remain at Drumcree Church expecting to be allowed to begin their permitted parade, which would pass along the mainly nationalist Garvaghy Road in Portadown.
However, protesters have maintained a presence at the side of the road, insisting that the parade should not be allowed to proceed.
Lawyers for the Garvaghy Road Residents Coalition have issued a fresh legal bid to prevent the Drumcree march, as crunch talks finished without a breakthrough.
The fresh application to the Court of Appeal in Belfast argues that the Parades Commission had "materially misdirected itself" on the police assessment of the potential for disorder and had not given an "accurate representation of the evidence received from PSNI" in its decision.
International moderator 'likely the direction we're going in' - McEntee
Ms McEntee said earlier that she thought the appointment of an outside mediator would be a welcome move.
She said: "It's very clear that this has been very difficult for all communities in Northern Ireland. It's been a very difficult few days for the residents on the Garvaghy Road and it has been difficult for all political parties.
"I want to acknowledge and commend the restraint that has been shown, and to call for continued calm. It's really important that people engage, that is the only way we will find a solution through this.
"I expect today that there will be further engagement with the community. I expect there will be further engagement with the Orange Order.
"I hope to see a process put in place that will allow people the time and space.
"People have been up late at night. It has been a very challenging time, particularly for the community, and it is really important that this is resolved through dialogue, but also it's really important that people in the community do not have a march forced on them, where very clearly this is not something that people want."
Mr Martin informed the Dáil that the Irish Government remained in constant contact with their British counterparts as efforts to find a solution continue in Belfast.
Alastair Power, the Orange Order's deputy district master in Portadown, is among a small group of lodge members who have remained at Drumcree Church.
He said: "We are still at the stalemate from 8am on Sunday morning.
"The police are still giving us an assessment that they cannot police us safely down the Garvaghy Road.
"We have left it with them that we are here and waiting until they can give us safe passage to complete our 1998 parade, which was given to us by the Parades Commission with 35 Orangemen, under really restrictive conditions from the Parades Commission, but we accepted that and we wish to bring our banner back home.
"Let's see what's on the table and hopefully everybody can come and get this done, and resolved for everyone."
Breandán Mac Cionnaith of Garvaghy Residents' Association speaks at protest last night
Meanwhile, the ongoing row is expected to feature again during exchanges at Stormont tomorrow.
Northern Ireland's First Minister Ms O'Neill was accused by the Stormont speaker of showing "gross contempt" to the Stormont Assembly after she refused to answer an urgent question on her participation in an unlawful protest against the controversial parade.
Ms O'Neill and other senior Sinn Féin colleagues were among a large crowd that blockaded the road in the predominantly nationalist area of Portadown on Sunday to prevent the contentious Orange Order parade from passing the route.
Under parading laws in Northern Ireland, protests must be notified to, and approved by, the Parades Commission adjudication body.
Police confirmed yesterday that the protest was unlawful as the commission had not been notified about it.
Ms O'Neill said today that police have not contacted her about her attendance at the protest and that she does not expect to be arrested over the incident.
Orangemen have attempted to begin their parade on a number of occasions, but police have halted them.
The PSNI has defended its approach and Assistant Chief Constable Ryan Henderson said the use of force to move protesters off the Garvaghy Road risked people getting "seriously hurt".
The Drumcree parading dispute, which was associated with violent disorder during the Troubles, has been reignited after the Parades Commission granted permission for a limited parade down the Garvaghy Road for the first time in almost 30 years.
At the height of the blockade on Sunday, more than 1,000 people congregated on the road to prevent the parade from the Drumcree Church from passing along the route.
A ruling by the Parades Commission permitting the Orange Order march from Drumcree Church and along the Garvaghy Road was upheld in an "unprecedented" late-night sitting of the High Court in Belfast in the early hours of Sunday.
Read more:
Why the controversial Orange Order parade was approved
The Drumcree parade down the Garvaghy Road has been banned since 1998.
The stand-off in the late 1990s led to violent clashes for several summers and political tension necessitated major security operations.
The Orange Order has unsuccessfully applied for more than a quarter of a century to complete its 1998 walk along its traditional route.
On Friday, the commission reversed its long-running determination and granted permission for the parade, a decision welcomed by unionist parties and met with outrage from nationalist and republican parties.
Permission was granted for a parade subject to strict restrictions, including a limit of 35 participants and an 8am start time.
Follow live updates as residents remain on the Garvaghy Road
