The march had been due to travel along the largely nationalist Garvaghy Road for the first time in almost 30 years.
An Orange Order parade in Portadown has been delayed after thousands of protesters gathered on the Garvaghy Road and blocked the planned route.
Members of the Order had assembled at Drumcree Church this morning but remained there while discussions with the PSNI continued.
The march had been due to travel along the largely nationalist Garvaghy Road for the first time in almost 30 years.
The parade was allowed to proceed following a series of late-night court hearings, with the High Court ultimately dismissing a challenge to the Parades Commission decision.
Police have appealed for calm and warned those blocking the road that offences may be investigated.
Chief Constable Jon Boutcher said officers were dealing with an exceptionally challenging situation.
First Minister Michelle O'Neill has said the decision risks damaging confidence in the peace process, while Northern Ireland Secretary Chris Byrant has rejected that assessment.
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