"We support the right to peaceful protest and also we condemn violence and racism of any kind, and we call for a de-escalation of tensions," said Borrell.
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The EU's foreign policy chief has slammed the death of George Floyd as an "abuse of power".
Floyd died after being filmed lying on the floor in Minneapolis as a police officer had his knee on the 46-year-old's neck.
It has sparked days of protests and violence in the US, with demonstrations and outrage spreading to Europe.
Josep Borrell, the EU's foreign affairs minister, said: "We are shocked and appalled by the death of George Floyd."
He went on to say it was "an abuse of power" which he said "had to be denounced" and combatted in the US and elsewhere.
"We support the right to peaceful protest and also we condemn violence and racism of any kind, and we call for a de-escalation of tensions," said Borrell. "Allow me to repeat that all lives matter, black lives also matter."
In Europe, citizens have taken to the streets in solidarity protests. In Amsterdam, Berlin, Dublin and London, thousands turned out to denounce police brutality. On Tuesday, another demonstration is scheduled in Paris.