Thousands of people took part in processions which shut down city centre roads and prompted counter-protests.
Up to 800 police officers were deployed to manage the event, which saw marches proceed through the city centre and past Catholic churches.
Members of Call It Out, a campaign group that opposes anti-Irish and anti-Catholic bigotry, held vigils outside churches on the routes.
Chief superintendent Mark Sutherland, divisional commander for Greater Glasgow, said: “We are aware that on a number of occasions today there have been outbreaks of racist and sectarian singing by some of those attending to support the Orange Order processions, this is utterly unacceptable and we completely condemn this behaviour.
“Where possible, we are seeking to take action against those intent on causing harm and dividing our communities, we have already made arrests in connection with various offences and will continue to do so where required.
“With large crowds gathering today, our main priority has been public safety and to ensure minimum disruption to the wider public.”
— Police Scotland (@policescotland) September 18, 2021
He added: “Once again, we see a number of people intent in causing offence and stirring up hatred by singing unacceptable sectarian and racist songs, I want to again condemn this behaviour in the strongest possible terms.
“It is clear that sectarianism remains a serious, ongoing problem in Scotland and whilst policing has an important role in tackling this type of behaviour, this is a collective problem and needs to be addressed in a collective, collaborative manner.”
The Church of Scotland took to Twitter as the marches took place to condemn anti-Catholic bigotry.
It said: “The Church of Scotland opposes anti-Catholic bigotry and sectarianism. We have a very close working relationship with the Roman Catholic Church.
“Over the years we have worked together to tackle sectarianism and support one another.
“We speak to leaders in the Roman Catholic Church every week and greatly appreciate the friendship that exists between our churches and our communities.”
Crowds lined the streets in the city centre for the marches including on George Street and West George Street, and there was a large police presence at Glasgow Green where members of the parades gathered in the afternoon.
Glasgow City Council said 32 roads in the city had been closed off for the processions until the mid-afternoon.
In 2018 a Catholic priest was attacked outside St Alphonsus’ Church in the city as an Orange walk marched past.
Call It Out said its supporters had gathered outside St Benedict’s in Easterhouse and Blessed John Dun Scotus in the Gorbals as marches went past to “say no to hatred on the streets of Glasgow”.
Writing on Twitter, it added: “Our resolve is stronger than ever and those willing to stand with us are growing in number. No to anti-Catholic marches past Catholic churches No to institutional anti-Catholicism.”