In a statement on Saturday afternoon Archbishop Eamon Martin called for “prayers and support for a peaceful resolution to complex Garvaghy Road situation”.
The Catholic primate said he shared the “sense of shock and disappointment of so many people at recent developments”.
“I also appeal for support for the patient use of solely lawful and democratic processes to resolve this deeply complex and emotive situation.”
Fr Peter Clarke, from St John the Baptist in Portadown, said he was concerned the march would “clash” with parishioners coming and going from the church.
He said he had emailed the commission to express his concerns and stated he “doesn’t know how they came to” their conclusion.
Parishioners at St Patrick’s Church on William Street are also likely to be affected ahead of the 10:00 service, according to the priest.
He added “tensions are high” in the community, and said he will be addressing the situation during Sunday’s service.
The decision to give the go-ahead for the parade came after the five-person Parades Commission, led by Prof Evelyn Collins, held face-to-face talks with the Orange Order earlier this week, and a separate meeting with the residents’ coalition.
Senior police officers were also consulted about the planned parade.
Within the 31-paragraph determination by the Parades Commission, details were revealed of conversations held with the PSNI.
The document stated: “The police made both written and oral submissions, indicating that they, at the time of making them, had no information indicating that the parade would result in disorder or violence.”
The Police Service of Northern Ireland (PSNI) said it had activated “mutual aid arrangements to support contingency planning for a policing operation” in Portadown on Sunday.
It is understood about 200 officers are coming from Scotland.
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