DETROIT » A white Detroit police detective who called the Black Lives Matter movement “racists” and “terrorists” has been demoted, the police chief said today.

Nate Weekley is also the brother of a Detroit officer who was charged with involuntary manslaughter in the accidental shooting of a black girl during a raid years ago.

Weekley was disciplined after posting remarks on Facebook in response to the fatal shooting of five officers in Dallas last week. He wrote that he had considered taking a day off after the “outrageous act perpetrated against my brothers.”

“The only racists here are the … Black Lives Matter terrorists and their supporters,” said Weekley, who also used a crude word to describe the group as excrement.

He has been demoted to officer from detective during an internal investigation, said Chief James Craig, who informed Mayor Mike Duggan.

“When we voice an opinion contrary to the department’s mission, the department’s goals, that’s a problem. … Social media can be our friend. But if you want to inject personal opinions, we will take quick and prompt action,” Craig said.

He said the department also is investigating online comments by a black police supervisor. He declined to elaborate.

Detroit is 80 percent black. Across the country, the deaths of unarmed black males by police have inspired protests under the Black Lives Matter moniker. Craig noted there was a peaceful demonstration in the city Friday night.

Police union president Mark Diaz, who talked to Weekley, said officers are under pressure. He acknowledged the chief has the power to demote the detective. The union would represent Weekley in any disciplinary phase if appropriate.

“I’m not going to comment on whether it was wrong or right,” Diaz said of the online post. “In a perfect world we would contemplate the reality of what anyone says in a public forum and how it affects others.”

Weekley’s brother, Joseph Weekley, was leading a raid on a Detroit home in 2010 when he accidentally pulled the trigger and killed a 7-year-old girl. A judge dismissed a charge of involuntary manslaughter during a second trial in the highly publicized case.

Separately, Detroit police arrested four people in an investigation of online threats to kill white officers. Craig said the results of the probe will be given to prosecutors.

Although possibly a joke, “I take it serious,” the chief said of threats.