By Sam Levin in San Francisco, Zach Stafford in Chicago, Scott Bixby in New York and Matthew Weaver in London

Vermont senator vows to work with president-elect on helping workers but oppose him elsewhere, as demonstrations take place in cities across country

Bernie Sanders speaks during a rally for Hillary Clinton before the US election. Photograph: Patrick Breen/AP

Bernie Sanders has acknowledged that Donald Trump managed to become US president by tapping into the anti-establishment anger of “a declining middle class” but said he will continue to challenge him.

As thousands of people crowded into streets in major cities to protest against Trump’s victory, Sanders, who defied expectations by running a close race against Hillary Clinton for the Democratic nomination, said he was prepared to work with the president-elect to help working families.

But the self-styled “democratic socialist” said he would “vigorously oppose” the “sexist, xenophobic and anti-environment policies” that featured prominently in Trump’s campaign.

Sanders, the senator from Vermont, reluctantly backed Clinton in her doomed bid for the presidency after a hard-fought Democratic campaign in which the two repeatedly clashed as he portrayed her as a member of a discredited elite.

Many commentators attributed Sanders’s popularity, particularly among young people, to anger at the establishment after the financial crash of 2008.  In his post-election statement Sanders noted that Trump also harnessed that resentment.

The statement said: “Donald Trump tapped into the anger of a declining middle class that is sick and tired of establishment economics, establishment politics and the establishment media.”

Sanders added: “People are tired of working longer hours for lower wages, of seeing decent paying jobs go to China and other low-wage countries, of billionaires not paying any federal income taxes and of not being able to afford a college education for their kids – all while the rich become very much richer.”

It concluded: “To the degree that Mr Trump is serious about pursuing policies that improve the lives of working families in this country, I and other progressives are prepared to work with him.

“To the degree that he pursues racist, sexist, xenophobic and anti-environment policies, we will vigorously oppose him.”

As US voters and international leaders began to come to terms with a Republican White House led by the former reality television star, people opposed to Trump held peaceful rallies on Wednesday against the racism, sexism and xenophobia that they say the president-elect has made mainstream.

Demonstrations were held in cities including New York City, Chicago, San Francisco, Oakland, Philadelphia and Seattle.

As night fell in midtown Manhattan, people took over Sixth Avenue and marched by Trump Tower, carrying signs that read “Not my president”, “She got more votes” and “Hands off my pussy”, a reference to a leaked recording where Trump bragged that he could sexually assault women because of his fame. A number of arrests were made.

Protesters who had marched all the way from Union Square – some 35 blocks downtown – continued past Trump Tower, with a crowd congregating in front of the president-elect’s building.

“Fuck your tower! Fuck your wall!” people chanted at Trump Tower’s brass-escutcheoned facade, as scores of NYPD officers manned barricades, behind which stood eight Department of Sanitation trucks filled with dirt.

Protesters gather near Trump Tower during a march against the president-elect in Manhattan on Wednesday. Photograph: Eduardo Munoz/Reuters

Thousands also took to the streets in Chicago, a Democratic city that overwhelmingly supported Clinton according to initial polls.

Gathering for what activists called an “emergency Trump protest”, demonstrators virtually shut down the city during rush hour traffic as they shouted: “Trump is not my president.”

Several larger demonstrations throughout the day were led by high school and college students, including a massive walkout at a high school in Berkeley, California.

Protests also launched in Pennsylvania, Arizona, Oregon and other states in regions throughout the US. By evening on the west coast large rallies began to emerge in Seattle and Oakland, organised under the hashtag #NotMyPresident.

Sanders’s reaction to Trump’s victory echoes many on the left who have been alarmed by Trump’s extremist statements, but share the apparent rage of his supporters against the elite.

In Britain, the Labour leader, Jeremy Corbyn, said: “Trump’s election is an unmistakable rejection of a political establishment and an economic system that simply isn’t working for most people. It is one that has delivered escalating inequality and stagnating or falling living standards for the majority, both in the US and Britain.”

He added: “This is a rejection of a failed economic consensus and a governing elite that has been seen not to have listened. And the public anger that has propelled Donald Trump to office has been reflected in political upheavals across the world.”

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