"I know you know that black lives matter," Meghan said in a video she recorded for students graduating from her old high school in Los Angeles which was aired on Wednesday (June 3).
The death of Floyd has become the latest flashpoint for long-simmering rage over police brutality against African Americans and led to nationwide protests, some violent, with curfews imposed in some cities to quell the disorder.
The duchess, a former U.S actress and wife of Queen Elizabeth's grandson Prince Harry, said she wanted to say "the right thing" and was nervous her words would be "picked apart".
Britain's royal family by tradition does not comment on political issues. However, Meghan and Harry stepped down from their official royal roles at the end of March and are now living in Los Angeles with their baby son Archie.