The force has come in for criticism since a number of people protesting against the monarchy were arrested during events to commemorate the late monarch in Scotland.
During the proclamation of King Charles III in Edinburgh, a 22-year-old woman was arrested in connection with a breach of the peace after an anti-monarchy sign was held up. A 22-year-old man was arrested in connection with the same offence after the Duke of York was heckled as he walked in a procession with the Queen’s coffin in the city.
A third man, 74, pleaded guilty to breach of the peace near the Palace of Holyroodhouse and received a £350 fine, and other incidents received publicity.
Speaking in Holyrood on Wednesday, Keith Brown praised the work of the police during the operation – dubbed Operation Unicorn – but said he would talk to Chief Constable Sir Iain Livingstone in a meeting on Thursday.
“I am not able to comment on individual cases but I do confirm that Police Scotland do approach their job firmly on the basis of human rights legislation and operate, of course, under the principle of policing by consent,” he said in response to a question from Labour MSP Katy Clark.
“They have confirmed there will be a formal debrief process for Operation Unicorn and I understand that Operation Unicorn will be discussed at the Scottish Police Authority board later this month – the appropriate forum for doing that.
“I also understand this will include reviewing at least one of the incidents that took place while the operation was active.
“I am meeting with the chief constable tomorrow and will discuss these issues with him with a view to looking at, as ever, what lessons can be learned from the operation and how these can be applied to future policing operations.
“I will also congratulate him and his force on a superb job, notwithstanding the issues which have been raised by the member.”
It is not clear which of the incidents will be reviewed, nor what the outcome of such a review may be.
Ms Clark said media reports around the arrests had suggested the tactics employed by the police were “heavy-handed”.
Meanwhile, Scottish Green MSP Maggie Chapman has written to Sir Iain to express her concerns over the arrest.
“Free speech and the right to protest are cornerstones of our democracy,” she wrote.
“I passionately believe in the importance of each of these rights, even if the views expressed by people exercising them are views with which I disagree.
“I am also of the firm belief that, in a functioning democracy, views that run contrary to those of the establishment should be allowed to be expressed, as long as they do not incite hate.
“Police Scotland has the responsibility and duty to protect the rights of all people in Scotland, not just those in power or in leadership positions.”
A spokesman for Police Scotland said: “The chief constable will provide an update on Operation Unicorn at the Scottish Police Authority board meeting on September 29. We will respond to correspondence in due course.”