Both these movements would have failed if there wasn't a violent component demonstrating the alternative if they didn't choose the more peaceful route.

If you want more context on how the two method supported each other in the civil rights movement, here's a good book.

It's important to note that King didn't unilaterally condemn violence, he acknowledged that they were a response to a greater, ongoing injustice, and that the white moderates who pretended to agree with their aims, but opposed them because of their methods were as much if not a greater barrier to civil rights than the klanman.