Police put up metal security fences around US President-elect Donald Trump's new Washington hotel on Thursday and a line of concrete blocks shielded the front of New York's Trump Tower as cities around the country braced for a second day of protests over his election.

A day after thousands of people took to the streets in at least 10 US cities from Boston to Berkeley, California, chanting “not my president” and “no Trump,” fresh protests were planned for the nation's capital, Baltimore and Madison, Wisconsin.

A Trump campaign representative did not respond to requests for comment on the protests but Rudy Giuliani, the former New York City mayor and a high-profile Trump supporter, called the demonstrators “a bunch of spoiled cry-babies.”

“If you're looking at the real left-wing loonies on the campus, it's the professors not the students,” Giuliani said on Fox News on Thursday. “So these are the ones who are more influenced by the professors .... Calm down, things are not as bad as you think.”

The protesters, mostly young people, blasted the New York real estate developer for campaign rhetoric critical of immigrants, Muslims and allegations of sexual abuse of women. More than 20 people were arrested for blocking or attempting to block highways in Los Angeles and Richmond, Virginia, early Thursday morning.

A protective barrier of Sanitation Department trucks are parked in front of Trump Tower (Getty)

Police officers walk in front of Trump Tower, the home of President-elect Donald Trump (AP)

Outside the gilt Trump Tower, where Trump lives, 29-year-old Alex Conway stood holding a sign that read “not my president.

“This sign is not to say he isn't the president of the United States, but for two days I can use my emotion to be against this outcome and to express that he's not mine,” said Conway, who works in the film industry. “The only thing I can hope for is that in four years I'm proved wrong.”

New York City Police and sanitation trucks, block off Trump Tower (AP)

In Washington, one jogger shouted an expletive about Trump as he passed the Trump International Hotel on Thursday, just blocks from the White House, where the former reality TV star had his first meeting with President Barack Obama to discuss transition plans.

More anti-Trump demonstrations are planned heading into the weekend, according to organisers' online posts. One urged protesters to rally in Washington, D.C., on Inauguration Day, Jan. 20.

Supporters of Trump, who surprised many in the political and media establishment with Tuesday's win, urged calm and recommended that Americans wait to see how he performed as president.

On Wednesday night, protests in Los Angeles and Oakland, California, each drew several thousand people. More than a dozen people were arrested by Los Angeles police when demonstrators tried to block a major highway intersection, a local CBS affiliate reported. The Oakland demonstrators blocked traffic, threw objects at police and smashed store front windows.

The United States has seen waves of large-scale, sometimes violent protests in the past few years. Cities from Ferguson, Missouri, to Berkeley have been rocked by demonstrations following high-profile police killings of unarmed black men and teens. Those followed a wave of large-scale protest encampments, starting with the Occupy Wall Street movement in New York in 2011.

Trump said in his victory speech, which was delivered in a far calmer manner than he displayed in many campaign appearances, that he would be president for all Americans. Some of his most controversial campaign proposals, including the call to ban Muslims from entering the United States, had been removed from his campaign website by Thursday.