Police Scotland will carry out additional patrols around statues this weekend to try to curb vandalism.
After Black Lives Matter protests raised calls for some sculptures to be removed, several across Scotland were damaged.
This includes the statues of both Henry and Robert Dundas, the 1st and 2nd Viscount Melville respectively, which were damaged in Edinburgh.
Henry Dundas worked to frustrate efforts to end the slave trade by using his influence as home secretary, setting the move back 15 years.
Assistant chief constable Kenny MacDonald said Police Scotland will be carrying out additional patrols around the statues over the weekend while protests are taking place.
Mr MacDonald said: “We are aware of a small number of events scheduled to take place this weekend, however, our firm advice remains that people should find alternative ways to protest rather than attending mass gatherings – for example, through digital means.
“I am aware that vandalism of a small number of monuments and statues has taken place in recent days.
“Such action is criminal and will be fully investigated.
“Police officers will be providing additional patrolling around such monuments and statues in the coming days to deter such criminality.”
He added: “We understand that people want to make their voices heard but they must do so lawfully and peacefully.
“We would encourage everyone to continue to follow the Scottish Government’s regulations and guidance to help the collective effort to protect the NHS and save lives.
“There will be an appropriate policing plan in place for the coming days and into the weekend.”