As millions marched in cities across the US in a resounding show of defiance against the inauguration of Donald Trump, protesters vowed that the fight had just begun.

Women’s Marches swept from the canyons of New York to the National Mall in Washington, one day after Trump was sworn in as the nation’s 45th president.

The demonstrations were an opening salvo against a president whose divisive words on the campaign trail – against women, immigrants and Muslims – will not soon be forgotten by a brewing resistance movement.

“This is only the beginning,” Evvie Harmon, global coordinator for the Women’s March, told the Guardian. “We are not going away.

“This is a mass mobilization and we are going to take this network of people and we are going to get them to lobby their members of Congress, call their governors … it’s going on from here”.

Harmon said organisers’ initial estimates indicated that the march in Washington exceeded a million participants while the movement attracted at least 3 million men and women worldwide.

The huge turnout in the nation’s capital – some inbound flights in recent days were filled almost entirely with women marchers – prompted the event to spill well beyond the official route and clog the city’s main arteries.

Protesters erupted in cheers and chants as they marched, as cars passing by honked in approval.

“I think it’s really powerful to walk,” said one marcher, Jenny Moyrila, who carried a neon-pink sign that read “Wanna Be Starting Somethin’”.

“But then you have to find people hopefully to connect with, to keep on speaking about the issues that matter.”

'This is just the beginning': women who marched against Trump vow to fight on