Portland police are also investigating a report of a shooting and a possible injury on a Willamette River bridge which protesters had been heading towards.
On Friday night, tear gas was used in response to “burning projectiles” thrown at officers by protesters in Portland.
Hundreds of people marched through the city, disrupting traffic and spray-painting graffiti. Authorities said vandalism and assault had taken place during the demonstration, which organisers had billed as peaceful earlier in the day.
In other parts of the country, spirited demonstrations on college campuses and peaceful marches along city streets have taken place since Wednesday.
Hundreds of people also joined a Friday afternoon “love rally” in Washington Square Park in Manhattan. Evening marches also disrupted traffic in Miami and Atlanta.
More than 1,000 protesters took to the streets across California after night fell including in Los Angeles, where more than 200 were arrested a night earlier.
In Bakersfield, where Mr Trump is far more popular than in the rest of the state, some held signs reading “Anti-Trump, Pro-USA”.
Small protests were also held in Detroit, Minneapolis, Kansas City, Missouri, Olympia, Washington and Iowa City.
More than 200 people, carrying signs gathered on the steps of the Washington state Capitol. The group chanted “not my president” and “no Trump, no KKK, no fascist USA”.
In Tennessee, Vanderbilt University students sang civil rights songs and marched through campus across a Nashville street, temporarily blocking traffic. A protest also occurred in Minneapolis.
In Chicago, multiple groups planned protests throughout Saturday.
Demonstrations also were planned for Saturday in Las Vegas, Los Angeles and other areas.
Previous demonstrations drew thousands of people in New York and other large urban centres. The largely peaceful rallies were overshadowed by sporadic episodes of vandalism, violence and street-blocking.
Earlier, President-elect Mr Trump raised eyebrows when, after he had repeatedly vowed on the campaign trail to repeal the Affordable Care Act “on day one,” said he would be open to maintaining portions of Barack Obama’s signature legislative achievement.
Mr Trump told The Wall Street Journal that, after speaking with Mr Obama at the White House the day before, he was considering keeping the clause that allows children to stay on their parents’ insurance policies.
In a separate interview with CBS’ 60 Minutes, he said: “It happens to be one of the strongest assets.”
He has previously said he may keep the prohibition against insurers denying coverage because of patients’ existing conditions.
He also said that he wants “a country that loves each other” but said he did not regret his incendiary rhetoric during the campaign against Democratic candidate Hillary Clinton, telling the Wall Street Journal: “No. I won.”
Mr Trump shook up his transition team as he plunged into the work of setting up his administration, elevating Vice President-elect Mike Pence to head the operation.
The move, one of the first key decisions as Mr Trump moves from campaigning to governing, amounted to a demotion for New Jersey Governor Chris Christie, who had been running the Republican’s transition planning for months.
On the heels of Mr Trump’s surprise victory this week, his team has begun to embark upon building a government, an enormous undertaking that probably requires him to alter his hands-on management style and consider going outside his small, insular group of loyalists.
He has been scrambling to identify people for senior White House jobs and Cabinet posts, a huge task that must be well in hand by the time Mr Trump is inaugurated on January 20.
For Mr Trump, who ran on a pledge to “drain the swamp” of Washington insiders, the team is strikingly heavy on those with long political careers.