Taking a knee, banging drums and ignoring social distancing measures, outraged protesters from Sydney to London on Saturday kicked off a weekend of global rallies against racism and police brutality.

The death at police hands of George Floyd, an unarmed black man in the US state of Minnesota has brought tens of thousands out onto the streets during a pandemic that is ebbing in Asia and Europe but still spreading in other parts of the world.

"It is time to burn down institutional racism," one speaker shouted through a megaphone at a hooting crowd of thousands outside the parliament building in London.

"This is how we take care of each other," she added after urging everyone to pull on a face mask. "This is how we stay alive."

Officials around the world have been trying to balance understanding at people's pent-up anger with warnings about the dangers of a disease that has officially claimed nearly 400,000 lives globally.

Yet tens of thousands of Australians defied Prime Minister Scott Morrison's call to "find a better way", and thousands more in Britain ignored the health minister's warning that the "coronavirus remains a real threat".

"We want justice! We want to breathe!" hundreds chanted in Tunis, as demonstrations convulsing US cities spilled out across the world.

Dressed in black

"Are you sure of your silence," asked a poster of a man laying a pink rose at a memorial set up outside the president's office in Pretoria, South Africa.

In Sydney, aboriginal protesters performed a traditional smoking ceremony at the start of a "Black Lives Matter" protest, which was sanctioned at the last minute after initially being banned on health grounds.

Many held up signs and wore face masks marked up "I can't breathe" -- the words Floyd kept repeating while handcuffed as a policeman knelt on his neck.

One placard simply read "8:46" -- the amount of time the 46-year-old was pinned to the ground by the white officer before his death.

"The fact that they have tried to push us all back and stop the protest, it makes people want to do it even more," said Jumikah Donovan, one of thousands who turned up thinking the Sydney ban was still in place.

Floyd's death came during the spread of a disease that has disproportionately affected black people and ethnic minorities in global centres such as London and New York.

It also came in the throes of a historic economic downturn that has statistically affected the poor and marginalised the most.

This confluence, and accompanying outrage at US President Donald Trump's partisan response, has refocused attention on the world's racial divides like few other events since the 1960s.

The US embassy in London said it stood "united with the British public in grief".

"We welcome this exercise of free speech, which contributes to constructive dialogue, education and change," it said, adopting a more conciliatory tone than the one taken by Trump.

"There remains much work to be done."

Thousands defy bans 

Memorial events and peaceful tributes were to stretch in Europe from Warsaw to Lisbon on Saturday, before shifting to major US cities and to Montreal in Canada.

In Paris, police banned a rally scheduled outside the US embassy compound and another near the Eiffel Tower.

But on Tuesday, another banned rally in Paris drew more than 20,000 people in support of the family of Adama Traore, a young black man who died in police custody in 2016.

There were also events scheduled Saturday in Amsterdam, and in Madrid on Brussels on Sunday -- as well as for the second weekend running across the United States.

Tens of thousands were expected in Washington, where Mayor Muriel Bowse renamed the area outside the White House "Black Lives Matter Plaza".

With tensions soaring, several US police departments launched investigations into officers who were recorded hitting, pushing or baton-charging protesters and some reporters -- including foreign ones.

The protests have even resonated in war-scarred countries such as Iraq, where the "American Revolts" and the Arabic phrase for "We want to breathe, too" hashtags are spreading on social media.

"I think what the Americans are doing is brave and they should be angry, but rioting is not the solution," said Yassin Alaa, a 20-year-old camped out in Iraq's protest-hit Tahrir Square.