Hope appeared to emerge from fear among Donald Trump’s opponents at the weekend as up to two million people around the world, mostly women, staged protests against the new US president and proclaimed the birth of a new political movement.

In raucous but peaceful scenes, more than half a million joined the Women’s March on Washington DC in what was thought to be the largest ever inauguration protest, dwarfing the 60,000 who protested against the Vietnam war before Richard Nixon re-took office in 1973.

“Welcome to your first day, we will not go away!” they chanted in the direction of the White House.

More than 600 “sister marches” took place across the US and around the globe with 250,000 reported to have gathered in Chicago, and around 100,000 each in Los Angeles and Boston. In New York, 400,000 anti-Trump activists marched past Trump Tower on Fifth Avenue, according to the office of the Democrat mayor, Bill De Blasio. Around 100,000 people also mobilised in London, with other smaller marches in countries including Australia, New Zealand, Germany, France, Hungary, Switzerland, Czech Republic and Canada.

The organisers of the main Washington march had said the purpose was to send a message that “we expect elected leaders to act to protect the rights of women, their families and their communities”. But the protesters’ concerns spread wider.

Placards outside the US embassy in London’s Grosvenor Square read: “Dump Trump”, “Reject hate, reclaim politics” and “No to racism, no to Trump”. In Berlin, where the country has welcomed refugees from Syria, protesters chanted: “No hate, no fear, immigrants are welcome here.”

“Trump typifies toxic masculinity, I understand why the march has this name and we are happy to march underneath that,” said Carson McColl in London who was marching with his partner with a banner saying “The Pussy Grabs Back” – a reference to Trump’s 2006 remark that he grabs attractive women by the genitals.

In Paris, at least 7,000 gathered near the Eiffel Tower holding up banners that read “liberty, equality, sorority” in a reference to France’s national motto.

Organisers said the surprising turnout – so large in Chicago, that organisers had to cancel the march portion of their event for safety reasons – plus the “heartening and galvanising” tone of the gatherings should now provide a springboard for long-term political action against what they see as Trump’s divisive politics.

As the feminist writer Gloria Steinem put it in a speech in Washington, this was “the upside of the downside” of Trump’s election. “This is more than just a single day of action, this is the beginning of a movement,” the organisers of the Washington march said on Sunday.

That sentiment was echoed in London. Emma McNally, an artist who co-orgainsed the march that packed Trafalgar Square with five times more people than originally expected, said: “It was peaceful and it was hopeful and people felt galvanised that now is the time to act.”

The events provided a counterpoint to Friday’s inauguration when a small minority of protesters communicated their outrage at the Trump presidency through violence. Two hundred and seventeen people were arrested and six police officers sustained minor injuries in Washington as black-clad anti-fascists vandalised shop windows, smashed a limousine and threw stones at police officers.

Trump was forced to address the wave of peaceful protests on Sunday.

Watched protests yesterday but was under the impression that we just had an election! Why didn't these people vote? Celebs hurt cause badly. — Donald J. Trump (@realDonaldTrump) January 22, 2017

The marches were indeed a magnet for A-list celebrities. Helen Mirren, Courtney Cox, Cynthia Nixon and Whoopi Goldberg were among the actors protesting in New York. In Washington Alicia Keys sang Girl on Fire and Madonna gave a profanity-laced address. “Yes, I’m angry,” Madonna said. “Yes, I’m outraged. Yes, I have thought an awful lot about blowing up the White House. But I know that this won’t change anything.”

Michael Moore, the documentary-maker, flipped the most reverberant phrase of Trump’s inauguration speech and said: “We are here to end the Trump carnage.” The singer Cher said Trump’s ascendance has people “more frightened maybe than they’ve ever been”.

While the marches were peaceful, they also showed up the political divisions in America. Marlita Gogan, a Trump supporter who came to Washington from Houston, Texas, for the inauguration, said police had advised her family not to wear their “make America great again” hats as they walked through crowds of protesters on Saturday.

“I think it’s very oppressive,” she said of the march atmosphere. “They can have their day, but I don’t get it.”

And the marches were smaller in states where Trump dominated the November polls. Several thousand showed up in Cincinnati, Ohio. An estimated 1,000 people turned out in Milwaukee in Wisconsin.

Brietbart, the right-wing news website formerly run by the new White House chief strategist, Steve Bannon, wrote about the protesters’ “largely incoherent message that asks for nothing reasonable – the only thing they seem to be demanding is that President Trump go away, something that will not happen”.

But the overall large turnouts were perhaps not surprising given a recent ABC News/Washington Post poll found Trump had the lowest favorability rating of any incoming US president since the 1970s.

“The only source of light on this miserable day is the massive, multi-racial, multi-generational progressive resistance movement led by women and people of colour that’s already emerging to confront Donald Trump’s agenda of hate, and [which is] growing stronger every single day,” said Democracy for America’s executive director, Charles Chamberlain, in a statement following the inauguration ceremony.

Protesters outside the US made clear that they were marching not just in solidarity with Americans but because of their concerns about changing politics in their countries.

McNally said “corresponding characters” to Trump in British politics, including the former leader of Ukip, Nigel Farage, show that danger of similar forces taking hold in the UK is real. “It is critical that each and every one of us now acts to engage in their local politics and local community and stand for equality in any way we are able,” she said. “It is an exciting opportunity. Rarely has the enemy shown its face so clearly.”

Natasha Blok, 30, had joined the London protest because 2016 had been “a wake-up call”. “It is amazing to feel this solidarity,” she said. “I feel like this is history in the making. I want to be able to tell my future children that I was here.”

Kate Allen, director of Amnesty International UK, said of the marches: “This is more than a moment. This is a movement and people of all genders, all ages and all backgrounds are coming together to take action against attacks on human rights and women’s rights.”

• This article was amended on 24 January 2017 to clarify Kate Allen’s job title.