Khan congratulated those who protested peacefully on Saturday, but said those who turned violent “gave up on the cause”.
“The brutal murder of George Floyd must be a catalyst for change in the world.”
He added: “No country, city, police force or institution can take responsibility for doing better.
“We must unite and eliminate racism wherever it is found. Black Lives Matter.
“To the small minority who were violent and threw glass bottles and flares – you endangered a safe and peaceful demonstration and abandoned this important cause.”