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4 year oldMr Floyd died in Minneapolis on 25 May, after a policeman knelt on his neck even as he said he could not breathe.
There have been protests across the US since, but Washington's police chief believes Saturday's "may be one of the largest we've ever had in the city".
Anti-racism rallies have also been taking place in other countries.
Parliament Square in central London was filled with people supporting the Black Lives Matter movement, despite calls by the British government to avoid mass gatherings for fear of spreading the coronavirus.
In Australia, there were major protests in the cities of Sydney, Melbourne and Brisbane that focused on the treatment of indigenous Australians.
Mr Floyd, an unarmed black man, died after being arrested outside a shop.
Video footage showed a white police officer, Derek Chauvin, kneeling on Mr Floyd's neck for almost nine minutes while he is pinned to the floor. Mr Floyd is heard repeatedly saying "I can't breathe".
Mr Chauvin has been dismissed and charged with murder. Three other officers who were on the scene have also been sacked and charged with aiding and abetting.
Almost a dozen different demonstrations have been advertised by organisations and activists, according to local media.
Protesters have been asked to gather at landmarks such as the Lincoln Memorial and the Capitol, and some are expected to march towards the White House.
"We have a lot of public, open source information to suggest that the event on this upcoming Saturday may be one of the largest we've ever had in the city," Metropolitan Police Department Chief Peter Newsham told journalists.
He did not provide a crowd estimate, but Army Secretary Ryan McCarthy said local officials were projecting that between 100,000 and 200,000 people would attend, the Associated Press reported.
On Friday, Washington Mayor Muriel Bowser, who has clashed with President Donald Trump over his handling of the protests triggered by Mr Floyd's death, asked for the withdrawal of all federal law enforcement officers and National Guard troops from the city's streets.
In recent days, it had become apparent that their presence was "unnecessary" and "may counterproductive to ensuring the protesters remain peaceful", she said.
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