A letter from the force's divisional commanders to local representatives says they have been dealing with an "increasingly crowded protest landscape" over the last few weeks.
While many of these demonstrations are "legitimate", broader solutions are needed to deal with the issues they raise, it says.
Protests and counter-protests in George Square, Glasgow, required significant police resources, the letter says.
Disorder broke out in the square on June 17 when far-right loyalists disrupted an event supporting refugees.
The letter says: "Like so many people in Scotland, the chief constable and officers of Police Scotland were shocked about recent events in the United States.
"Racism in all its forms is disgraceful and unacceptable.
"Those events do not reflect our style of policing in Scotland and we continue to value the strong bond of trust with all our citizens and communities."
It adds: "Although many of these protests are entirely legitimate, they pose significant challenges for policing, and public safety risks, given the ongoing pandemic in Scotland.
"Some of these protests have required a very significant resource deployment from Police Scotland and those are officers who are no longer available to deal with other policing demands.
"There is also no easy policing solution to issues and grievances which often have deeper roots in wider social and political issues, or which act as proxies for ingrained sectarianism."
The letter urges councillors to take an active role, saying: "Given the risks to social cohesion posed by this increasingly crowded protest landscape, and the negative impact on the overall capacity of Police Scotland, we would ask that you would exert the influence that you have, as elected politicians, to seek broader solutions to this growing issue of concern to Police Scotland."
Commenting on the letter, one senior officer said the current level of deployments is "unsustainable".
Deputy chief constable Will Kerr said: "In the midst of responding to the coronavirus pandemic, we have also had to deploy significant numbers of officers to police the growing number of protests and counter-protests that we've seen in recent weeks.
"Those officers are being taken away from the communities they serve at a time when crime is starting to return to levels that are more in line with what we experienced before the lockdown.
"This is unsustainable, but policing on its own can't provide the answers to deep-rooted issues and we need the whole of civic Scotland to step forward into that space."
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