Donald Trump has responded to huge protests against his presidency at the weekend, suggesting many demonstrators did not vote.

Mr Trump took to Twitter to question the protesters’ motives, before later adding that he supported their right to be heard.

“Watched protests yesterday but was under the impression that we just had an election! Why didn’t these people vote? Celebs hurt cause badly,” Mr Trump tweeted.

“Peaceful protests are a hallmark of our democracy. Even if I don’t always agree, I recognize the rights of people to express their views.”

It is estimated more than two million people in the US and around the world took part in protests against Mr Trump’s presidency, dubbed ‘Women’s Marches’.

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.

Pop icon Madonna made an unannounced stage appearance in Washington, welcoming marchers to “the revolution of love, to the rebellion. To our refusal as women to accept this new age of tyranny”.

“It took this horrific moment of darkness to wake us the f**k up,” she said.

“Let’s march together through this darkness and with each step know that we are not afraid, that we are not alone, that we will not back down.”

See the amazing pictures of the women’s marches here

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

Mr Trump initially downplayed the size and significance of the marches, using his old Twitter account rather than his POTUS handle.

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

Two hours later on Sunday he changed his tune.

Peaceful protests are a hallmark of our democracy. Even if I don't always agree, I recognize the rights of people to express their views.

— Donald J. Trump (@realDonaldTrump) January 22, 2017

The Washington rally attracted over 500,000 people by the unofficial estimate of city officials – apparently more than Mr 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 and overwhelmed the subway system.

“We want a leader, not a creepy tweeter,” some marchers chanted, while others shouted: “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 Mr 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.

More people attended the Washington march than Mr Trump’s inauguration. Photo: Getty

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 people marched past Mr 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. Washington prosecutors said about $100,000 in damage had been done and 230 adults and five minors had been arrested.

The global marches began in Australia and New Zealand on Saturday, About 3000 marchers gathered at Hyde Park in Sydney before marching towards the US consulate.

“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.

Sydney staged one of the first global marches in solidarity. Photo: AAP

US singer-songwriter Amanda Palmer, Wiradjuri elder Jenny Munro and social commentator and writer Jane Caro were among the women who appeared 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.

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.

About 2000 women, men and children marched peacefully in Auckland, Wellington, Dunedin, Christchurch and Invercargill.

– with AAP