More than one million people have rallied at women’s marches in the US and cities around the world to send President Donald Trump an emphatic message on his first full day in office that they won’t let his agenda go unchallenged.

Many of the women came wearing pink, pointy-eared “pussyhats” to mock the new president. Plenty of men joined in, too, contributing to surprising numbers everywhere from New York, Philadelphia, Chicago and Los Angeles to Mexico City, Paris, Berlin, London, Prague and Sydney.

The outpouring served to underscore the degree to which Trump has unsettled people in both hemispheres.

“We march today for the moral core of this nation, against which our new president is waging a war,” actress America Ferrera told the Washington crowd.

“Our dignity, our character, our rights have all been under attack, and a platform of hate and division assumed power yesterday. But the president is not America … We are America, and we are here to stay.”

The Washington rally attracted over 500,000 people by the unofficial estimate of city officials – apparently more than Trump’s inauguration drew on Friday.

Turnout in the capital was so heavy that the designated march route alongside the National Mall was impassable.

Protesters were told to make their way to the Ellipse near the White House by way of other streets, triggering a chaotic scene that snarled downtown Washington.

The day after Oresident Trump’s inauguration, thousands marched in Washington (above) and in New York (below) as well as hundreds of other cities around the world.

“We want a leader, not a creepy tweeter,” some marchers chanted. Others: “Welcome to your first day, we will not go away!”

Around the world, women brandished signs with slogans such as “Women won’t back down” and “Less fear more love.” They decried Trump’s stand on such issues as abortion, health care, diversity and climate change. And they branded him a sexist, a bully, a bigot and more.

In Chicago, organisers cancelled the march portion of their event for safety reasons after the overflow crowd reached an estimated 150,000. People made their way through the streets on their own anyway.

Thanks for standing, speaking & marching for our values @womensmarch. Important as ever. I truly believe we're always Stronger Together.

— Hillary Clinton (@HillaryClinton) January 21, 2017

In New York, well over 100,000 marched past Trump’s home at glittering Trump Tower on Fifth Avenue. More than 100,000 also gathered on Boston Common, and a similar number demonstrated in Los Angeles.

Gloria Steinem at #WomensMarch: "If you force Muslims to register, we will all register as Muslims." https://t.co/a6B3LAjPIo

— MSNBC (@MSNBC) January 21, 2017

All told, more than 600 “sister marches” were planned worldwide. Crowd estimates from police and organisers around the globe added up to more than a million.

“I feel very optimistic even though it’s a miserable moment,” said Madeline Schwartzman of New York City, who brought her twin 13-year-old daughters to the Washington rally. “I feel power.”

#indigenouswomenrise rounddance before the #WomensMarch on DC. #IndigenousRising pic.twitter.com/ZJpb11J6BR

— Dallas Goldtooth (@dallasgoldtooth) January 21, 2017

The rallies were a peaceful counterpoint to the window-smashing unrest that unfolded on Friday when self-described anarchists tried to disrupt the inauguration. Police used pepper spray and stun grenades against the demonstrators. More than 200 people were arrested.

The hand-knit “pussyhats” worn by many women served as a message of female empowerment, inspired by Trump’s crude boast about grabbing women’s genitals.

The global marches began in Australia and New Zealand on Saturday, About 3,000 marchers gathered at Hyde Park in Sydney before marching towards the US consulate.

“Feminism is my Trump card”, ”Girl Power vs Trump Tower and “fight like a girl,” were among the placards held by marchers.

About 3000 gathered in Sydney for a women’s march on Saturday.

A Sydney marcher has a message for the new US President.

“We’re not marching as an anti-Trump movement per se, we’re marching to protest the hate speech, the hateful rhetoric, the misogyny, the bigotry, the xenophobia and we want to present a united voice with women around the globe,” organiser Mindy Freiband said.

US singer-songwriter Amanda Palmer, Wiradjuri elder Jenny Munro and social commentator and writer Jane Caro are among the women who will appear at the Sydney march.

Ms Caro told the crowd: “I don’t hate anyone, but I’m not fond of Donald Trump.”

A group of Trump supporters paid thousands of dollars to have the president’s name written in the Sydney sky above the protesters.

In the skies above Martin Place, Sydney #WomensMarch pic.twitter.com/QBxVAh6CFS

— Jess Hill (@jessradio) January 21, 2017

About 300 protesters also rallied in Brisbane’s CBD to “unite against hate”.

A handful of Trump supporters also attended the march but were drowned out with chants of “racists aren’t welcome here”.

Events are also taking place in Melbourne, Canberra.

New Zealand launched the first of the post-inauguration marches, hours after the world watched Mr Trump be sworn in as the 45th President of the United States.

We shall overcomb!!! #WomensMarch #WMNewZealand #whyIMarch #WM_global #WMW pic.twitter.com/Bcu4PGUU4I

— Women's March NZ (@WMNewZealand) January 20, 2017

About 2,000 women, men and children marched peacefully in Auckland, Wellington, Dunedin, Christchurch and Invercargill.

Marchers carried signs reading “we shall overcomb”, “girls just want to have fundamental rights” and “love trumps hate”.

– with AAP