Glasgow City Council's public processions committee gave the Black Skull Corps of Fifes and Drums the option of joining in with another parade before making their way to celebrations marking the Battle of the Boyne on Saturday.
The band had applied for 30 people to take part in a parade from the east end to Glasgow Cathedral before 9am to mark the anniversary of the band's first engagement in marching from the site of the former Orange Order headquarters.
They have taken part in the procession since 2002.
Police Scotland said the march would put extra pressure on its stretched resources and has lodged objections to the council. At yesterday's meeting council officials gave more details on the risk to safety and public order, the excessive burden on policing and disruption to the community in relation to the date and route of the procession submitted.
Minutes from the meeting state: "The committee agreed that the procession should take place on a revised date to be agreed between the organiser, Police Scotland and council officers or if agreement can be reached by the organiser to join other parades to satisfy their requirements."
Police will be taken off duty from as far afield as Stirling, Fife and Edinburgh to be deployed at this weekend's major Orange Order march, the first big parade in Scotland since the creation of the national force.
Almost 750 officers will be committed to the city's streets to police the annual Boyne celebrations, with rest days also cancelled to control the event.
There will be 57 parades through Glasgow next Saturday, as about 4500 members of the Orange Order and tens of thousands of supporters gather for the organisation's biggest event outside of Northern Ireland.
Another parade in Coatbridge will see over 10,000 members of the Protestant loyal orders and bandsmen march. The cost of policing the Glasgow event alone will be more than £500,000 despite the Orange Order using its own members to steward the parade.
Referring to Saturday's County Grand Lodge of Central Scotland event in Coatbridge, Chief Superintendent Nelson Telfer, divisional commander of Lanarkshire division, warned participants involved in any anti-social behaviour, or drinking outdoors would be severely dealt with.
County grand master and North Lanarkshire councillor Charlie Cefferty said: "We recognise that an event of this magnitude is a huge challenge and to assist Police Scotland, the Orange Order has trained over 2000 stewards which will allow them to focus on normal police activity."