In an emotional pleas, the mother of Floyd's daughter demanded justice for him, saying he was a good father who did not deserve to die face down on the pavement, pinned under the weight of three police officers.
With her 6-year-old daughter Gianna clinging to her, Roxie Washington told reporters she wants all four officers involved in Floyd's death to be held accountable for his death.
"At the end of the day, they get to go home and be with their families," Washington said. "Gianna doesn't have a father. He will never see her grow up, graduate. He will never walk her down the aisle."
Washington's Catholic archbishop has strongly criticised President Donald Trump's visit to a shrine as civil unrest continues in the US over the death of a black man in police custody.
The visit "misused" and "manipulated" the Saint John Paul II National Shrine, Archbishop Wilton D Gregory said.
He said he found the president's action "baffling and reprehensible".
Filmmaker Spike Lee told the BBC anger over George Floyd's death and systemic injustice are fuelling protests.
On Monday Mr Trump threatened to send in the military to quell disturbances, vowing to "dominate the streets", as protests sparked by the killing of Mr Floyd, 46, in Minneapolis continued.
The president said he would deploy the army if cities and states failed to control the protests. But on Tuesday at least one mayor rejected the use of National Guard and military forces.
Democratic presidential hopeful Joe Biden criticised Mr Trump for using the crisis to appeal to his supporters, saying he was "serving the passions of his base".
On Tuesday the Las Vegas sheriff said an officer died in a shooting after police attempted to disperse a crowd, and four officers were injured on Monday in St Louis, Missouri.