WASHINGTON (AFP) - More than two million people flooded the streets of US cities on Saturday (Jan 21) in a peaceful day of women-led protests a day after the inauguration of President Donald Trump, according to estimates from march organisers.

At the main "Women's March on Washington" organisers told AFP they estimated the turnout at one million, with huge crowds joining sister marches around the country - and tens of thousands more marching worldwide.

It was not possible to independently verify the claim as the US capital does not release crowd counts.

Metro operator WMATA told the Washington Post it had moved a record 470,000 passengers in the hours leading up to the march, a weekend ridership record.

More than half a million people also swarmed the streets of Los Angeles in one of the largest rallies by protesters, who fear that progress on gender equality, contraception and abortion could be chipped away under Trump.

LAPD spokesman Andrew Neiman said his department was still working on a crowd estimate but he told AFP it was certainly larger than a pro-immigration march which drew 500,000 in 2006.

The Los Angeles march's organisers claimed a turnout of 750,000. March organizers in New York also claimed a crowd count of half a million, tweeting: "This is what democracy looks like! Over 500k people are here at @womensmarch!"

Roused by fiery speeches, the women sent out a resounding message of resistance and activism the day after Trump took office with a vow to roll back the policies of former president Barack Obama.

"I know that we can do better, we have to fight for the change we want to see," said Michelle Phillips, a 45-year-old recent American citizen, who told AFP she came to take a stand against what she called Trump's "platform of hate and bigotry."

WARNING: STRONG LANGUAGE

The Chicago Tribune reported that 150,000 rallied in the city, although the figure was not confirmed by police. And in Boston, local media cited Mayor Marty Walsh's office as estimating the crowd between 135,000 and 150,000 people.

Huge gatherings were also reported in Miami, Denver and Seattle and Philadelphia, just a few of the dozens of sister marches planned around the country.

The call was heard far beyond US shores, with organisers saying over 2.5 million people signed up online to take part in one of more than 600 marches being held worldwide.

One of the largest was in London, where tens of thousands of women, men and children marched chanting "Dump Trump" and waving banners "Our Rights Are Not Up For Grabs - Neither Are We."

Organisers estimated the turnout for the main "Women's March on Washington" at half a million, double initial expectations.

Washington's Metro stations were overwhelmed as trains packed to bursting moved cheering, clapping marchers into the city.

By 11am, the city's Metrorail system said it had moved 275,000 people, more than most weekdays and eight times a typical Saturday.

The tide of women in knitted pink hats appeared to dwarf the throngs of Trump supporters in red "Make America Great Again!" caps who the day before had cheered the Republican's swearing-in.

Trump's defeated rival Hillary Clinton tweeted her support to the crowds massed around Washington's National Mall, as actresses, feminists and liberal politicians took the stage to vow resistance to Trump.

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

Former secretary of state John Kerry was spotted in the crowd - a day after leaving office - with his dog on a pink leash.

Women made up the overwhelming majority of the people who arrived in Washington, hooting and cheering on jam-packed trains and buses.

Many carried homemade signs. "Keep your tiny hands off me," said one. "Rise, Love, Resist," read another.

Trump - and his new administration - were feted at balls after an inaugural speech that painted a grim vision of national decline under his Democratic predecessor Barack Obama, punctuated by the new president's vow to stop "this American carnage."

For his first full day in the world's most powerful office, Trump attended a multi-faith service at Washington National Cathedral. He was later due to visit the headquarters of the CIA, an agency he feuded with bitterly before taking office.

Trump's inaugural speech on Friday set the tone for his presidency: proudly populist, fiercely nationalist and determined to break with Obama's legacy.

His first act in office - signing an executive order aimed at freezing Obama's signature health-care law - was a potent gesture in that direction, with more such actions expected to follow on Monday.

But if Friday was Trump's day - marred by sporadic outbreaks of vandalism and more than 200 arrests - Saturday belonged to demonstrators with fresh memories of his fat-shaming a former beauty queen, sex assault allegations and a controversial stance on abortion.

The knitted "pink pussyhats" they wore were an allusion to his boasts in a leaked videotape of grabbing women's private parts with impunity.

Actress Scarlett Johansson urged: "I feel that in the face of this current political climate it is vital that we all make it our mission to make it very, very personal."

Filmmaker Michael Moore, a march organiser, noted that his copy of the Washington Post was bannered with the headline "Trump Takes Power." "I don't think so. Here is the power," he said, gesturing to the crowd.

TV actress America Ferrara told the crowd, "The platform of hate and division assumed power yesterday. But the president is not America. We are America. And we are here to stay."

Jennifer Behr, a 42-year-old accessory designer, rode a packed train from Baltimore to make her voice heard.

"It's important we assert our majority and we have a large physical presence to show Trump and the Republicans that they cannot railroad our country," she said.

While Trump won 42 per cent of the women's vote, millions who did not vote for him worry that gender rights and other progress on women's health, contraception and abortion could be chipped away.

The Women's March began with a simple Facebook post from Hawaii grandmother and retired lawyer Teresa Shook to about 40 of her friends - but word travelled quickly and the event took on a life of its own.

Dozens of progressive groups backed the march, as well as Amnesty International and Planned Parenthood, the women's health care provider that is a Republican target because of the abortion services it provides.