A metal security fence has been erected around Donald Trump's new Washington hotel, while concrete blocks surround Trump Tower in New York, following nationwide protests over the outcome of the US presidential election.

Trump's victory with 279 Electoral College (EC) votes to Hillary Clinton's 228 EC votes prompted student walkouts in several colleges in California, while in other west coast cities thousands took to the streets chanting: "Not my president".

Damage to property has been reported, along with graffiti and small fires, in what have largely been peaceful protests against the Republican president-elect.

Although Trump's campaign has not yet issued a statement in response to the gatherings across the country – which included a demonstration outside Trump Tower in New York City – former New York mayor Rudy Giuliani, who is tipped for a cabinet post, dismissed the protesters as "a bunch of spoiled cry babies".

He told Fox News: "If you're looking at the real left-wing loonies on the campus, it's the professors not the students.

"So these are the ones who are more influenced by the professors.... Calm down, things are not as bad as you think."

More protests have been planned for the weekend, with security stepped up around several buildings linked with the Republican, Reuters reported.

However, Trump's victory speech indicated he is hoping for unity in a country so divided following the election campaign, with a pledge to represent all Americans.

His plea for unity was also echoed by Clinton during her concession speech and in a comment on the protests by President Barack Obama, who acknowledged people's right to peacefully protest, but expressed hopes of a reconciliation between those who voted for opposing candidates.