In New York, thousands of protesters gathered at the Barclays Center, and police arrested dozens of protesters at the massive demonstration in the Brooklyn area.
About 1,000 people participated in a protest in the city of Alantana, which witnessed violence, as fire broke out in the city center near the headquarters of CNN News.
Hundreds of protesters in Minneapolis violated a curfew and gathered in the streets around a police station that was torched last night.
"We are here because we are a generation who know that things have to change," said Paul Selman, a 25-year-old black man.
In Detroit, hundreds of protesters joined a "march against police brutality" outside the city's public safety headquarters and chanted "No justice, no peace."
Similar protests also broke out in Denver cities, where a highway was closed.
In Houston and Louisville, Kentucky, clashes erupted as a number of residents demanded justice for Briona Taylor, a black woman who was killed by police in her apartment in March.
In its turn, Washington witnessed hundreds of people demonstrated, on Friday evening, outside the White House in an expression of their anger after the killing of Floyd.
During their gathering in front of the White House, the demonstrators demanded "justice for George Floyd", waving slogans including "Stop killing us" and "Black lives are important."
Detroit city police said today, Saturday, that one person was killed after gunmen shot at protesters in the killing of George Floyd, an African American.
A representative of the Attorney General in Minnesota had announced earlier that the authorities had arrested the police officer who had knelt Floyd's neck, after 3 nights of violent protests that shook the city of Minneapolis.
The policeman was charged with unintentional killing Friday, prosecutors said.
Prosecutor Mike Freeman told reporters, "Former police officer Derek Chauven has been charged with unintentional murder by the Hinpin District Prosecutor's Office," AFP reported.
For its part, the Floyd family considered that this procedure was late and insufficient, and said in a statement that it wanted to charge "the premeditated murder charge" of that policeman, adding, "We want to see the arrest of the other police officers involved in the case."
For his part, former US President Barack Obama counted on Friday that the death of George Floyd should not be considered "a normal matter" in the United States.
As for President Donald Trump, he revealed on Friday that he had spoken to the Floyd family, and said in the White House, "I understand the pain," adding, "The George family has the right to justice."