Erdogan's comments are likely to irritate Turkey's NATO ally, with relations between the two countries already strained over their differing stances on the Syria conflict.
Rioting has broken out in several US cities over this incident and several others where police have killed black men.
"The racist and fascist approach that led to the death of George Floyd in the US city of Minneapolis as a result of torture has not only deeply saddened all of us, but it has also become one of the most painful manifestations of the unjust order we stand against across the world," Erdogan tweeted in English.
"I believe that the perpetrators of this inhumane act shall receive the punishment they deserve," said Erdogan."We will be monitoring the issue."
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