Police Scotland has expressed its "disappointment" with Black Lives Matter campaigners who attended events across the country.
Protests involving hundreds of people took place in Glasgow and Edinburgh, while anti-racism activists held a rally in Aberdeen on Saturday.
The march was the latest sparked by the death of George Floyd in the US city of Minneapolis while in police custody last month.
But officers have expressed concern over a lack of social distancing at the rallies in the midst of the Covid-19 crisis.
Assistant Chief Constable Kenny MacDonald said: “I am disappointed that some people chose to ignore the advice and attended a number of the events across Scotland.
“However for those who did attend, I would like to thank you for conducting your protest in a peaceful manner.
“An appropriate policing response was put in place for the events and these passed without significant incident.
“We would encourage everyone to continue to follow the Scottish Government's regulations and guidance to aid the collective effort to protect the NHS and save lives by preventing the virus from spreading.”
Hundreds of people - including military veterans - converged on George Square in Glasgow to protect the war memorial.
The event was organised by the Loyalist Defence League (LDL) to stop vandalism to the Glasgow Cenotaph, erected to commemorate the lives of those who died in the First World War.
There was also a heavy police presence with at least 12 visible officers and a number of police vans stationed around the square.
The LDL was penned in on the east side of the square, with a similar sized area reserved for counter-protesters which remained empty.
Some protesters across Britain have defaced memorials in recent weeks including a statue of Edward Colston, that was dropped into the city's harbour, due to his involvement in the slave trade.
A video posted on the Twitter page of the LDL said: “These war memorials and monuments have been built to remember and respect the many people who have paid the ultimate sacrifice in maintaining the very same liberties, justice and freedom that these thugs claim they're fighting for."
The video claimed an "orgy of violence" was expected this weekend, and it called on people to "help protect each and every one of them that is under threat".
A 62-year-old man was arrested and charged with a minor public order offence which took place close to, but was not associated with, the demonstration in Edinburgh.
He was held in custody and is due to appear in court on Monday.
