Chief Superintendent Mark Sutherland, Divisional Commander for Greater Glasgow, has condemns the alleged racist and sectarian behaviour ‘by some of those attending to support’ the marches.
Chief Superintendent Sutherland added that Police Scotland has already made arrests in connection with various offences and will continue to do so where required.
It comes as up to 13,000 people are expected to converge in the city centre on Saturday to ‘commemorate the 200th anniversary of the first Battle of Boyne parade’.
The senior officer continued: "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.
"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."
More than 30 Protestant parades will be taking part in the march with planned protests from campaigners against anti-Catholic and anti-Irish discrimination protesting against the event.
Around 800 police officers are expected to be out policing the Orange Order processions.
On Saturday morning, Police Scotland advised the public of traffic disruption and road closures with up to 32 road closures in place till mid-afternoon.