The activities they were criticizing were his actions in leading protests in favor of civil rights. Specifically, the white clergymen who wrote the letter (read it here) that King was responding to were criticizing King for his part in protests against segregation in Birmingham. The clergy wanted King and other black people to be more patient and to rely on the courts to give them the rights they seek. The white clergy allege that the direct actions of King and the other protestors will stir up hatred and violence.
Basically, then, what the "fellow clergymen" were asking King to do was to stop stirring things up. They wanted him and the rest of the black community to work through normal channels like the courts and the elected leaders rather than pushing forcefully for their rights.