What do you mean, "started to lean towards the more militant segments"? He was trying to reach out to them in order to bring those elements to the realization of the inescapable truth--that violent resistance would only invite further violence on the part of the state and would undermine the righteousness of their cause. King did not ever modify his belief that nonviolence was the only legitimate strategy for resisting oppression.
Jerusalem light rail conductors striking over new train schedule (Haaretz)
from the article: The documentary that should make every decent Israeli ashamed