Tens of thousands of people took to the streets of London, Paris and other cities across the world chanting “dump Trump” in solidarity with US protesters, a day after America's new president was inaugurated.

In London, a largely female crowd, which also had many men and children, packed a Trafalgar Square rally in solidarity with women-led demonstrations throughout the United States.

“Our Rights Are Not For Grabs — Neither Are We” were among the banners held aloft, along with “We shall overcomb” and “Make bigotry wrong again”.

Hannah Bryant, a 34-year-old museum worker, brought her four-year-old daughter — both of them wearing the bright pink “pussy hats” worn by US demonstrators.

“I've been teaching her about equality and prejudice,” she said.

“It's a feeling of solidarity — not in our name,” said Jill Pickering, a 56-year-old American student.

“I'm angry — I didn't vote for Trump.”

Organisers said 100,000 attended the London march, although there was no independent verification as police do not give an estimate.

In Paris, at least 2,000 people gathered near the Eiffel Tower, holding up banners that read “liberty, equality, sorority”, in a reference to France's national motto.

“I am here for women and for all minorities because Trump is a threat to all humanity,” said a US national Kendra Wergin, who is in her mid-30s.

Andreia Rossi, a 39-year-old Brazilian, told AFP she was taking part “because I am a woman, but also because I want to protest against everything Trump represents.”

She added: “It's very dangerous, he has lied to all those who voted for him, and that can happen in France too.”

Right-wing populists and nationalist groups in France and elsewhere in Europe have been emboldened by Trump's victory as well as by Britain's vote last year to leave the European Union.

While Trump won 42 per cent of the women's vote in the US, many worry that gender rights and other progress on women's health, contraception and abortion could be chipped away.

'Bridges not walls'

In Barcelona, Rome, Amsterdam and Geneva too, protesters were enraged by Trump's derogatory remarks on women.

“We are here for women and for human rights,” one of a large contingent of American expatriate women told SkyTG24 news channel in Rome.

“This American says Trump go back to your own planet,” read a placard brandished by a protester.

“We must defend democratic values,” said Karen Olson, who organised the Swiss march, as motorists driving by honked their horns in support.

“When injustice becomes law, resistance becomes duty,” read a banner held up by a Barcelona protester.

“Make America sane again,” read a banner in Amsterdam.

In Budapest, up to 400 people gathered in solidarity with the Washington marchers. “Bridges not walls,” read one of their banners, a reference to Trump's threat to build a wall separating the United States from Mexico to stop migrants from entering the country — and to have Mexico pay for it.

In Berlin, hundreds rallied in front of the US embassy, chanting pro-migrant slogans in a nation that welcomed nearly a million people fleeing war and poverty in 2015.

“No hate, no fear, immigrants are welcome here,” they cried.

In Prague, protest organiser Johanna Nejedlova branded Trump's rhetoric “hateful”.

“We want to express our support for values such as democracy, human rights, ecology and women's rights,” she said.

There were also solidarity marches beyond Europe too, with protests in Johannesburg, South Africa, where marchers held up banners reading “Black lives matter” and “Love trumps hate”.

Anti-Trump protests also took place in Australia with several thousand marching in Sydney and Melbourne. And in New Zealand, hundreds joined demonstrations in the capital Wellington as well as in Auckland.