Crowds including Northern Ireland First Minister Michelle O'Neill of Irish nationalists Sinn Fein and the party's leader, Mary Lou McDonald, gathered in the rain on the Garvaghy Road overnight after Belfast's High Court dismissed an application by residents to stop the parade early on Sunday morning.
Annual attempts by the Protestant Orange Order to march through the area triggered unrest across the British-run region before the route was banned in 1998, the same year the Good Friday Agreement largely ended the three decades of violence known as the "Troubles".
"This is madness," McDonald told reporters on the road, a Catholic enclave in the largely Protestant town of Portadown.
"This, in fact, is primitive treatment of any community in the year 2026. It is intolerable."
British Prime Minister Andy Burnham called for calm on Sunday.
"I know it's a tense situation; we do appeal for calm on all sides," Burnham told the BBC.
"There have been big gains made in Northern Ireland and we don't want to see things go backwards."
He said he had spoken to Irish Prime Minister Micheal Martin on the matter on Saturday.
Northern Ireland's Parades Commission - which regulates marches in the British-run region - on Friday permitted a smaller-than-usual 35 people to take part in the march between 8am (0700 GMT) and 9.30am.
A small group of Orange Order members wearing traditional silk orange sashes and black bowler hats gathered elsewhere in the town but the march had not started by 9.30am.
A senior member told the BBC the group would wait for police to tell them the route was ready for them to start.
Police vans parked near the Garvaghy Road had earlier broadcast a warning anyone taking part in the protest was committing a criminal offence.
The Drumcree dispute exploded in the mid-1990s when, in the wake of ceasefires by Northern Ireland's main guerrilla groups, it became a symbol of the wider dispute between mainly Catholic nationalists, who consider themselves Irish, and Protestants loyal to Britain.
The Orangemen, who take their name from Protestant King William of Orange, who defeated deposed Catholic King James II at the Battle of the Boyne in 1690, say their parades are part of their Protestant cultural tradition.
While most of the parades that take place across Northern Ireland each year are uncontroversial, nationalists say parades such as Drumcree passing through Catholic areas are an offensive display of triumphalism designed to intimidate them.
McDonald and O'Neill called on the British government and police to intervene.
O'Neill said she had spoken to Britain's minister for the region and the Irish government.
The Irish government issued a statement saying it was very concerned about the situation and that its primary concern was to "avoid a return to the divisions of the past".
"I think that this brings into question how this whole peace process works," said O'Neill, whose party rules alongside the largest pro-British party in a devolved power-sharing administration that was a key part of the 1998 peace deal.
The governing Democratic Unionist Party, some of whose MPs stood alongside the Orange Order, said the march must be allowed to proceed.
"A first minister's duty is to uphold lawful decisions, not inflame opposition to them," DUP leader Gavin Robinson said in a statement.
Northern Ireland's police chief, Jon Boutcher, appealed in a statement for "everyone to remain calm and peaceful" and urged those with influence to encourage people to comply with the law and work with the police.
