The bureau said it was continuing to investigate what happened over the weekend and asked for people's help in identifying the individuals believed to be involved in the violence, many of whom had their faces obscured.
Police noted that Crime Stoppers of Oregon is offering rewards up to $2,500 for information about the situation that is reported to Crime Stoppers and leads to an arrest. Tipsters can remain anonymous.
Police said eight people were treated for injuries suffered on June 29, including three police officers. Another three people were treated at hospitals.
Three suspects were arrested over the weekend. Gage Halupowski, 23, was charged with multiple counts of assault, including on a public safety officer; James Stocks, 21, was charged with harassment; Maria Dehart, 23, was charged with disorderly conduct and harassment.
All three were suspected to be part of Antifa, a far-left group that openly advocates for and commits violence.
"Demonstration events are very fluid in nature and the management of these events is complex," said Assistant Police Chief Chris Davis in a statement.
"There are hundreds of peaceful free speech events in the city in a given year that do not result in violence. Unfortunately, today some community members and officers were injured. We are actively investigating these incidents to hold those responsible accountable."