Orangemen are threatening to walk to Drumcree church this year without permission for the first time since 1998.
The Orange Order has failed to notify the Parades Commission that it wants to parade there this summer.
It is required to submit a form known as an eleven-bar-one, to serve notice of its intention to parade.
The order has confirmed no form has been submitted before this month's deadline.
"At the moment, Portadown District has not submitted the eleven-bar-one form for the annual Drumcree church parade on Sunday, July 4," an Orange Order spokesman said.
In a statement, the Garvaghy Road Residents Coalition (GRRC) in Portadown said it believed the order had decided to "engage in a game of brinkmanship" with the Parades Commission and to "unnecessarily raise tensions in Portadown and elsewhere".
Sinn Fein MLA John O'Dowd, who is a member of the working group established by the First and Deputy First Ministers to examine parading, said he thought the order was "making a mistake".
"There is a danger of raising tensions in an area where if tensions were raised it could affect right across the north," he said.
He said for many people in Portadown the "Drumcree parade issue is over".
"Over the last 10 years it has largely been peaceful and both sides of the community can get on with their lives," he added.