Orange walks will be re-routed to avoid the church where a sectarian attack took place on a priest.
Glasgow City Council's leader has said if the Orange Order does not voluntarily change the route of parades, the council will "insist".
Susan Aitken said the council was strength-testing existing laws to prevent attacks like the one on Canon Tom White a week ago.
The Orange Order said it was "happy to discuss" a change.
Cllr Aitken urged the Orange Order to change the route of upcoming parades to avoid St Alphonsus' Church in the city's east end where Canon White was spat on and hit as an Orange Walk passed.
'Whatever steps necessary'
She said: "The sectarian hate crime that took place on Saturday (7 July) was revolting and I understand the depth of feeling shown in communities across the city and beyond.
"We are supporting the ongoing Police Scotland investigation wherever we can. However, I have to be clear that the council does not have any legal authority to introduce a blanket ban on Orange walks, or public processions by any other organisation.
"The council will continue to closely examine how it operates within the national legislation that governs public processions. It will listen to communities with concerns about any march by any organisation - and will look to its partners, including city MSPs, to do the same.
"In the meantime, I am acutely aware that further parades are scheduled in the area in the coming weeks - and have made it clear to officers that the council is prepared to take whatever steps are necessary to ensure those marches do not pass the scene of Saturday's incident."
A spokesman from the Orange Order said: "It's something we would be happy to talk about, and we have asked for a meeting with the council, police and the Catholic Church to discuss it, although we have yet to hear back."
Police continue to investigate the attack on Canon White.