The protesters lit fires in dumpsters and flames were seen inside the building, media said.
Social media footage showed people throwing stones at the building and debris on the street in flames.
Black Lives Matter protests have been held across the United States in recent months after the May 25 death of George Floyd, a 46-year-old African-American man, who died after a white police officer knelt on his neck for nearly nine minutes, Reuters reported.
“Portland Police has declared the gathering near the Multnomah Building a riot after individuals vandalized, repeatedly smashed first floor windows with rocks and threw burning material into an office,” the Multnomah County Sheriff’s Office said on Twitter.
The Multnomah Building houses county government operations.
Police said that failure to comply with its order to disperse could lead to arrests and use of tear gas, crowd control munitions and impact weapons.
Media reported that fire in the building was put out by the police.
There were no immediate reports of any injuries or deaths, but the Oregonian reported that there were two arrests.
A crowd of about 200 gathered in the city’s Colonel Summers Park late on Tuesday before marching through Southeast Portland streets, eventually arriving at the Multnomah Building, the Oregonian reported.
US Attorney General William Barr came under fire from Democratic lawmakers earlier this month for sending federal officers to disperse protesters in the city.
Republican Senator Lindsey Graham on Tuesday called for the Department of Justice to prosecute a group of people caught on videotape beating and kicking a man who crashed his truck near protests in Portland.
