A judicial review of the decision to halt an Orange Order parade route along the Garvaghy Road has been adjourned until Monday.
The unionist Orange Order said Northern Ireland secretary Sir Chris Bryant's decision was a "capitulation to the threat of mob rule and violence", and accused chief constable Jon Boutcher of an "abdication of responsibility".
It applied for an emergency judicial review, which was heard at the High Court in Belfast on Saturday afternoon.
But duty judge Denise McBride said it was not an emergency and that significant material was still to be obtained.
Sir Chris announced the ban on Friday, citing public safety reasons.
The parade - from Drumcree Church into Portadown, Co Armagh - was approved by the Parades Commission for 27 September.
It would have been the first time it had been down the mainly nationalist Garvaghy Road in almost 30 years.
However, a large number of residents blocked the route late into the night.
An Orange Order statement said its members had "maintained a dignified and resolute stand in the face of intimidation and intolerance".
It added: "Urgent meetings with both the secretary of state and chief constable will be sought in the coming days where their decision making and actions in this matter will be robustly challenged."
Sir Chris said recent talks between the two sides to find a compromise had failed.
He said he was acting "in the interests of wider public interest and safety" after the chief constable had asked him to review the decision of the Parades Commission.
"I heard the concerns of people on all sides, and I only regret that we could not reach a compromise on a way forward and that many residents across Portadown have felt anxious and worried," said Sir Chris.
"With this in mind, I call for all protests, rallies and demonstrations to be stood down. There is no excuse for a continued ratcheting up of tensions."
Nationalist parties Sinn Fein and the SDLP welcomed the move, as did Irish premier Micheal Martin, who said it would be a "considerable relief" to people on Garvaghy Road.
However, Democratic Unionist Party leader Gavin Robinson said anger at Sir Chris and the police chief was "totally justifiable".
"People everywhere expect the rule of law to be upheld and justice to be done," he said.
"It remains inexplicable that the rights of Portadown District were trumped by obstruction of the road alone. I don't believe that alone to be the case."
He urged authorities to disclose "in clear terms what violence was planned" and said there had been rumours firearms and "incendiary devices [were] being stocked up along the roadway".
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