Trump tweeted that the demonstrations that began hours after polls closed Tuesday night were "very unfair".
A large crowd protests President-elect Donald Trump in Denver, Colorado, on November 10.
Later, Trump sent a tweet expressing appreciation for protesters' passion for the country.
Several thousand demonstrators gathered in the centre of the western city.
But civil rights groups and police reported an uptick in attacks on minority groups, some by people claiming to support Trump. Oregon Transportation Department officials intermittently closed local portions of Interstates 5 and 84 as a precaution. "Police advising crowd this is an unlawful assembly", Portland police said on Twitter.
In Los Angeles, protests continued on Thursday - though not as big as Wednesday - as organizers claimed they were saving their energy for the weekend, The Los Angeles Times reported.
"We will use our large trucks to stop traffic from coming onto the freeways if we know that protesters are headed toward the freeway or if they are already on the freeway", said Kimberly Dinwiddie.
In Philadelphia, protesters near City Hall held signs bearing slogans like "Not Our President", "Trans Against Trump" and "Make America Safe For All".
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In San Francisco earlier Thursday, numerous marchers were African-American and Hispanic students. "There's plenty of division, and there's finger-pointing in both directions, but there were things that were said that were not partisan, about women, about our Muslim brothers and sisters, about immigrants".
Ashley Lynne Nagel, 27, said she joined a Thursday night demonstration in Denver.
The Rev. Al Sharpton, a civil rights leader from NY, said anti-Trump protesters should borrow a page from the playbook that Republicans used to oppose Obama's policies.
Hundreds of students stormed out of their classrooms Thursday in San Francisco and marched to the city's famed Fisherman's Wharf.
Protests have taken place in USA cities on both nights since the result of the election, which Mrs Clinton lost for the Democrats despite enjoying a lead in most opinion polls. "This is students taking their feelings and emotions and channeling them in a way that feels right to them".
Demonstrations were also planned Saturday in Las Vegas, Los Angeles and other areas.
Meanwhile, the Ku Klux Klan recently announced that it plans to hold a victory rally on December 3 in North Carolina to celebrate Trump's win. The crowd of anti-Trump protesters burned American flags and chanted, "That's not my president".
The Fort Worth protest drew a diverse crowd, with a 3-year-old and blacks, whites and Hispanics in attendance.
Republican National Committee spokesman Sean Spicer: "I hope that people get it out of their systems. but then they give this man that was just elected very historically and his new vice president an opportunity to govern".