West Midlands Police have asked people to be mindful of misinformation and rumour on social media after two protests took place.
About 50 people gathered near a Hindu temple in Coventry on Thursday. Earlier, 150 people met in Smethwick which resulted in minor disorder.
The reasons surrounding the protests are complex, police said, but added it was working with community leaders.
Unsubstantiated claims on social media can have a serious impact, it warned.
A spokesman said there had been several instances of fake news and unsubstantiated claims being spread on social media and messaging services.
Rumours a Dudley shopkeeper was involved in the protests, prompting him to be racially abused. The shopkeeper was not involved in the protest, police said.
Claims two young men were attacked in Oldbury during a protest. There have been no reports to police of it happening.
A picture of a police officer at a mosque being used to suggest police are not impartial. The picture was taken at the start of the month during a routine visit, police said.
Coaches from elsewhere reported to be arriving in the West Midlands on Wednesday night to cause problems. Police said this did not happen.
"We have local officers on the streets, and are engaging with faith leaders and other key stakeholders in our communities, to keep us informed and better understand how people are feeling," a police spokesman said.
"We have appropriate policing plans in place to deal with any further incidents should they occur, and will continue to closely monitor what is happening."