Dozens of demonstrators chanted as they marched through Peckham, in the south-east of the capital, wielding placards reading “solidarity” and “Black lives matter”.
Unrest and heated riots have engulfed the city of Minneapolis and swathes of the US since Monday, when Mr Floyd, 46, was killed while in police custody.
Distressing footage showed him pleading for air while handcuffed as a white police officer knelt on his neck for almost ten minutes.
Derek Chauvin, 44, the policeman who was filmed pressing Mr Floyd to the floor, was charged with third-degree murder and second-degree manslaughter on Friday.
Activists have taken to the streets of Atlanta, New York and outside the White House in Washington, crying out: “I can’t breathe,” in memory of Mr Floyd’s last words.
Unrest has overwhelmed US authorities for a forth night in Minneapolis, Minesota, with the state’s governor acknowledging that he does not have enough manpower to contain the chaos.
Meanwhile, Donald Trump fired off a series of tweets ridiculing people who protested outside the White House and praising the Secret Service who used shields and pepper spray to push them back.
Hundreds of people gathered on Friday night to protest against the police killing as well as Mr Trump’s response.
The president tweeted he watched from inside his residence as officers “let the ‘protesters’ scream & rant as much as they wanted, but whenever someone …. got too frisky or out of line, they would quickly come down on them, hard – didn’t know what hit them”.
Mr Trump said if the protesters had managed to breach the White House fence, “they would … have been greeted with the most vicious dogs, and most ominous weapons, I have ever seen”.
The US president ended the last of five tweets by saying, “Tonight, I understand, is MAGA NIGHT AT THE WHITE HOUSE???”
The professionally managed so-called “protesters” at the White House had little to do with the memory of George Floyd. They were just there to cause trouble. The @SecretService handled them easily. Tonight, I understand, is MAGA NIGHT AT THE WHITE HOUSE???— Donald J. Trump (@realDonaldTrump)May 30, 2020
Minnesota governor Tim Walz vowed on Friday to start taking a more foreful approach to the uproar.
However, by early on Saturday morning, Mr Walz said he did not have enough troops, even with some 500 National Guardsmen.
“We do not have the numbers,” he said. “We cannot arrest people when we are trying to hold ground.”
Mr Walz said he was moving quickly to mobilise more than 1,000 extra Guard members, for a total of 1,700, and was considering the potential offer of federal military police.
However, he warned that even that might not be enough, saying he expected another difficult night ahead.
The Pentagon has ordered the US army to put military police units on alert to head to the city on short notice, at Mr Trump’s request, insiders said.
Elsewhere, a man was shot dead in Detroit, police cars were attacked in Atlanta and skirmishes with officers were caught on camera in New York City.
Minneapolis police said shots had been fired at officers during the protests, but no-one was injured.
On Thursday, protesters torched a police station soon after it was abandoned by police and went on to burn or vandalise dozens of businesses.
The Minnesota Police and Peace Officers Association urged Mr Walz to accept any help.
“You need more resources,” the group said in a tweet. “Law enforcement needs leadership.”
Chauvin was also accused of ignoring another officer who expressed concerns about Mr Floyd as he pressed his knee into the victim's neck.
Mr Floyd had been arrested on suspicion of using a counterfeit twenty dollar bill at a store.
Chauvin, who was fired along with three other officers who were at the scene, faces more than 12 years in prison if convicted of murder.
A lawyer for Mr Floyd’s family welcomed the arrest, but said he expected a more serious murder charge, and wants the other officers arrested, too.
Prosecutor Mike Freeman said more charges were possible, but authorities “felt it appropriate to focus on the most dangerous perpetrator”.
Protests nationwide have been fuelled by outrage over Mr Floyd’s death and years of police violence against African Americans.
Protesters smashed windows at CNN headquarters in Atlanta, set a police car on fire and struck officers with bottles.
Large demonstrations in New York, Houston, Washington, DC, and dozens of other cities ranged from people peacefully blocking roads to repeated clashes with police.
“You are disgracing our city,” Atlanta mayor Keisha Lance Bottoms told protesters. “You are disgracing the life of George Floyd and every other person who has been killed in this country.”
A post-mortem examination said the combined effects of being restrained, potential intoxicants in Mr Floyd’s system and his underlying health issues, including heart disease, likely contributed to his death. It revealed nothing to support strangulation as the cause of death.
Mr Trump said on Friday that he had spoken to Floyd’s family and “expressed my sorrow”.
He called video of the arrest “just a horrible thing to witness and to watch. It certainly looked like there was no excuse for it”.
Attorney Benjamin Crump, who is representing Floyd’s family, asked to take custody of Floyd’s body for an independent post-mortem examination.
The doctor who will carry out the procedure is Michael Baden, former chief medical examiner of New York City.
He was hired to examine Eric Garner, a black man who died in 2014 after New York police placed him in a chokehold, and he pleaded that he could not breathe.
State and federal authorities also are investigating Mr Floyd’s death.