President-elect Donald Trump fired back on social media after demonstrators in both red and blue states hit the streets for another round of protests, showing outrage over the Republican's win.

Demonstrations occurred from Portland, Oregon, to Chicago, to New York and parts in between and each typically drew a few hundred people, less than the thousands that gathered in various protests that surged after it became clear Trump had won Tuesday's election.

Late Thursday night, Trump went on Twitter to take on the protesters.

Trump tweets: "Just had a very open and successful presidential election. Now professional protesters, incited by the media, are protesting. Very unfair!"

In Portland Thursday night hundreds of people marched throughout the city as protests turned violent, with people smashing store windows and lighting off firecrackers.

Police declared the protests a riot, said there were people with baseball bats in the crowd and told people via loudspeaker to move on.

Oregon Department of Transportation officials closed portions of Interstate 5 and Interstate 84 in the area intermittently as a precaution.

In Denver, protesters managed to shut down Interstate 25 near downtown Denver briefly Thursday night.

Denver police tweeted around 10 pm that demonstrators made their way onto the freeway and traffic was halted in the northbound and southbound lanes.

Police say the interstate was reopened about half an hour later as the crowd moved back downtown.

Earlier protests in Denver, Boulder and Colorado Springs on Wednesday and Thursday went off peacefully.

In San Francisco's downtown, high-spirited high school students marched through, chanting “not my president” and holding signs urging a Donald Trump eviction.

They waved rainbow banners and Mexican flags, as bystanders in the heavily Democratic city high-fived the marchers from the sidelines.

"As a white, queer person, we need unity with people of colour, we need to stand up," said Claire Bye, a 15-year-old sophomore at Academy High School. "I'm fighting for my rights as an LGBTQ person. I'm fighting for the rights of brown people, black people, Muslim people."

In New York City, a large group of demonstrators once again gathered outside Trump Tower on Fifth Avenue Thursday night. They chanted angry slogans and waved banners baring anti-Trump messages.

"You got everything straight up and down the line," demonstrator David Thomas said.

"You got climate change, you got the Iran deal. You got gay rights, you got mass deportations. Just everything, straight up and down the line, the guy is wrong on every issue."

Protesters briefly shut down interstate highways in Minneapolis and Portland, Oregon. In Philadelphia, protesters near City Hall held signs bearing slogans like 'Not Our President', 'Trans Against Trump' and 'Make America Safe For All'.

About 500 people turned out at a protest in Louisville, Kentucky and in Baltimore, hundreds of people marched to the stadium where the Ravens were playing a football game.

Hundreds of protesters demonstrated outside Trump Tower in Chicago and a growing group was getting into some shoving matches with police in Oakland, California.

Another protest was building in Los Angeles, where 28 people were arrested Wednesday for blocking traffic during a demonstration that also saw vandalism to some buildings and a news truck.

Los Angeles Mayor Eric Garcetti, a Democrat, condemned what he called a "very, very small group of people" that caused problems in that demonstration but said he was proud of the thousands more that peacefully protested.

"I actually thought it was a beautiful expression of democracy. I think it was a marvellous thing to see the next generation of this country get engaged and involved," he said at a news conference, adding that at one time in his life he might have joined them.

As expected, the demonstrations prompted some social media blowback from Trump supporters accusing protesters of sour grapes or worse, though there were no significant counter-protests.

Trump supporters said the protesters were not respecting the democratic process.

As of Thursday, Democrat Hillary Clinton was leading Trump in votes nationwide 47.7 per cent to 47.5pc, but Trump secured victory in the Electoral College.