The Orange Order has been accused of trying to stage a march along part of the disputed Garvaghy Road area.
The organisation has been banned for years from parading through the Catholic district in Portadown, Co Armagh.
Its long standing demands to be allowed to march the route became associated with mass violence that engulfed Northern Ireland throughout the late 1990s. But members of the Order are accused of entering part of the contested route, with marchers only turning back when police arrived at the scene.
Sinn Fein Assembly member for the area John O'Dowd, who is Education Minister in the Stormont power-sharing Assembly, condemned the Order.
"This evening the Portadown District assembled at Drumcree," he said. "There was no PSNI (Police Service of Northern Ireland) presence at the church. The Orange Order seemed to take this as a signal to take part in an illegal parade down Garvaghy Road."
He said the parade reached the Ballyoran area before police arrived and the Orange Order members turned back.
The Sinn Fein representative said tensions were high in the wake of the incident. He said the Orange Order Grand Master Edward Stevenson should explain his organisation's conduct.
"Let us now hear from Mr Stevenson, let him finally emerge into the media and tell the people what is going on with the Orange Order under his leadership," said Mr O'Dowd.
A police spokesperson said: "There was a notified parade (on Wednesday) evening in Drumcree Road, Portadown.Police have received reports that there were possible breaches of the Parades Commission determination in respect of this parade. Police are investigating the circumstances."
A spokesman for the Order said it would be making no comment until it knew the full facts of what happened.