NEW YORK/LOS ANGELES -  Authorities at two universities in California said police were investigating attacks against female Muslim students, one of which was described as a hate crime.

Both attacks came a day after Donald Trump was elected president at the end of a campaign during which the Republican was criticised for divisive and inflammatory language against Muslims.

In one of the incidents, two assailants confronted their victim at San Diego State University and "made comments about president-elect Trump and the Muslim community," according to campus police.

The woman had her purse, backpack and car keys stolen. She went to get help and returned to the scene with police officers, only to find her car had been stolen, police spokesman Ronald Broussard said.

The case was being investigated as a suspected hate crime as well as a strong-arm robbery and auto theft, Broussard said.

"Comments made to the student indicate she was targeted because of her Muslim faith, including her wearing of a traditional garment and hijab," university president Elliot Hirshman and interim police chief Josh Mays said in a joint statement.

San Jose State University police said in a statement they were investigating a similar attack against a female student at a campus parking garage.

A male assailant approached the victim from behind, pulling at the victim's head scarf, choking and throwing her off balance, according to the statement circulated to students.

"Campus officials are closely monitoring the situation as the investigation continues. No arrests have been made," university spokeswoman Pat Harris said in an emailed statement to AFP.

"We are, of course, very concerned that this has occurred on our campus. No one should experience this kind of behavior at San Jose State," she added.

New York University's Muslim Students Association issued a statement saying engineering undergraduates had arrived that morning to find "Trump" scrawled on the door of their prayer room.

The organisation said members were "realising that our campus is not immune to the bigotry that grips America."

A Muslim student at the University of Louisiana at Lafayette told police that she was attacked by two men, one of whom was wearing a white hat emblazoned with "Trump."

Donald Trump, meanwhile, broke the relative silence that had fallen over his often controversial Twitter account Thursday night to blame the demonstrations against his election victory on "professional protesters" who he says have been "incited by the media". "Just had a very open and successful presidential election," Trump tweeted. "Now professional protesters, incited by the media, are protesting. Very unfair!"

He posted the tweet amid the second day of anti-Trump protests in cities across the nation.

The tweet dismissing the protests as being professionally orchestrated and created by the media (it's not clear why the media would need to incite the protesters if they are professionals), seems to conflict with the conciliatory and unifying tone the president-elect had taken since his victory speech early Wednesday.

In fact, the tweet about the protesters came nine minutes after another one describing his "great chemistry" with President Barack Obama. "Melania liked Mrs O a lot!" he tweeted.

Mostly peaceful and orderly protests took place in at least eight cities following the Republican businessman's defeat of Democrat Hillary Clinton in Tuesday's election. Demonstrators have voiced concern Trump would harm Americans' civil rights.

But late-night vandalism and graffiti turned a march in Portland, Oregon, into what police described as a “riot.”

"Due to extensive criminal and dangerous behavior, protest is now considered a riot. Crowd has been advised," tweeted the Portland Police Department, who pointed the finger at "anarchists."

Thousands turned up in Portland's Pioneer Courthouse Square early in the night for a peaceful protest and march but, as the night wore on, individuals were seen vandalizing businesses and property in the city's Pearl District and throwing objects at police.

"Love the fact that the small groups of protesters last night have passion for our great country. We will all come together and be proud!" Trump tweeted early on Friday.

Trump's critics worry that his often-inflammatory campaign rhetoric about immigrants, Muslims, women and others - combined with support from the Ku Klux Klan and other white supremacists - could spark a wave of intolerance against minorities.

East Coast protests took place on Thursday in Washington, Baltimore, Philadelphia and New York, while on the West Coast, demonstrators rallied in Los Angeles, San Francisco and Oakland in California, and Portland, Oregon.

After Clinton conceded defeat early on Wednesday, Trump took a far more conciliatory tone than he had often displayed during his campaign, promising to be a president for all Americans. His campaign rejected a Klan newspaper endorsement days before the election, saying Trump "denounces hate in any form."

But civil rights groups and police reported an uptick in attacks on minority groups, some by people claiming to support Trump.

More anti-Trump demonstrations were planned for the weekend. Trump takes office on Jan 20, succeeding President Barack Obama.

At least 35 protesters were arrested in downtown Los Angeles after blocking traffic and sitting in the street, local media said. A smaller band of demonstrators briefly halted traffic on a busy Los Angeles freeway before police cleared them.

In San Francisco, more than 1,000 high school students walked out of classes on Thursday morning to march through the financial district carrying rainbow flags representing the lesbian, gay, bisexual and transgender communities, Mexican flags, and signs decrying Trump.

Dozens in Minneapolis marched onto Interstate 94, blocking traffic for at least an hour as police stood by.

In Baltimore, about 600 people marched through the downtown Inner Harbor area, with some blocking roadways by sitting in the street, police said. Two people were arrested.

In Denver, a crowd that media estimated to number about 3,000 gathered on the grounds of the Colorado state capitol and marched through downtown in one of the largest of Thursday's events. Hundreds demonstrated through Dallas.