The EU supports the right to peaceful protest, and it condemns violence and all forms of racism, EU foreign policy chief Josep Borrell told a news conference on Tuesday.
A week of protests, both violent and peaceful, followed the posting of video showing Floyd, 46, an unarmed black man, being pinned down in Minneapolis, Minnesota by a white police officer.
The police officer knelt on his neck for nearly nine minutes even though Floyd appeared to lose consciousness.
He died shortly after being taken to a hospital.
His last words were "I can't breathe," which became the slogan of the nationwide protests.
Floyd was killed by "asphyxiation from sustained pressure," an independent autopsy found Monday.