Assistant Chief Constable Ryan Henderson said the PSNI was doing “everything we can to maintain order and ensure the safety of everyone in that area”.
“I want to thank those officers from Police Services in England and Scotland who have been in Northern Ireland supporting our efforts over the past week,” he added.
“Finally, I want to repeat the Chief Constable’s appeal for calm and for all parties to refocus efforts on working to find a lasting resolution to this issue.”
Protesters remain on Garvaghy Road and the Orange Order has maintained a presence at Drumcree church after talks to end the parading dispute ended without agreement.
The Orange Order’s Portadown District said on Friday that its position “has been clear from the outset: we set out to complete our parade through lawful and peaceful means, and despite the provocation and threats we have faced, it remains our firm intention to continue on that path”.
“Our community has demonstrated considerable restraint, dignity and patience, and we strongly encourage everyone to continue conducting themselves lawfully and peacefully,” it added in a social media post, external.
It said “rounds of talks with the Secretary of State concluded last night without agreement” and the “District is now carefully assessing the position and considering its next steps over the coming days”.
The statement added that it remains “committed to pursuing a lawful and peaceful resolution”.
The Democratic Unionist Party (DUP) leader Gavin Robinson said he expects the criminal investigation into the unlawful blocking of Garvaghy Road to begin next week.
Earlier, Robinson said there had to be “consequences” for “people who are law makers who are acting as law breakers”.
First Minister Michelle O’Neill was among those who attended the protest. She has said she understands the law, but chose to “stand in solidarity” with residents.
Robinson said he expected the investigation to begin next week “but it needs the space to see it conclude as well”.
The fallout over the proposed Orange Order march – which is opposed by residents of the Garvaghy Road – has lasted since Sunday morning.
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.
Orangemen and Garvaghy Road residents met Northern Ireland Secretary Sir Chris Bryant at Hillsborough Castle on Thursday night but did not break their deadlock.
Speaking after Thursday night’s talks, Sir Chris told reporters: “I think this is the end of these conversations.
“We haven’t come to a settled agreement and it’s a shame but my door remains open.”
Breándan Mac Cionnaith, the chairman of the Garvaghy Road Residents’ Coalition, said there had been no “meeting of minds”.
Nigel Dawson, the Orange Order’s Portadown district master, said it “remains as it has been”.
