READ MORE: Thousands of New Zealanders march for women's rights

MORE: Uncertainty and division as new US president sworn in

UPDATED 11.58AM: 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.

"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. 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.

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."

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.

Hillary Clinton, who lost to Trump, took to Twitter to thank the participants for "standing, speaking and marching for our values."

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.