What is Kennedy referring to when he says he "had a member of my family killed ... "?

This was actually part of a longer portion of his speech to reporters in 1968 when Martin Luther King got killed. The complete version of this portion is, "For those of you who are black and are tempted to be filled with hatred and mistrust of the injustice of such an act, against all white people, I would only say that I can also feel in my own heart the same kind of feeling. I had a member of my family killed, but he was killed by a white man."

With this, he was trying to reach out to the black people not to hate white people and have a stereotypical view of white people from a negative perspective. He states that he had a family member killed as well by a white man.