The iterative consensus problem requires a set of processes or agents with different initial values, to interact and update their states to eventually converge to a common value. Protocols solving iterative consensus serve as building blocks in a variety of systems where distributed coordination is required for load balancing, data aggregation, sensor fusion, filtering, and synchronization. In this paper, we introduce the private iterative consensus problem where agents are required to converge while protecting the privacy of their initial values from honest but curious adversaries. Protecting the initial states, in many applications, suffice to protect all subsequent states of the individual participants. We adapt the notion of differential privacy in this setting of iterative computation. Next, we present (i) a server-based and (ii) a completely distributed randomized mechanism for solving differentially private iterative consensus with adversaries who can observe the messages as well as the internal states of the server and a subset of the clients. Our analysis establishes the tradeoff between privacy and the accuracy: for given ε, b > 0, the ε-differentially private mechanism for N agents, is guaranteed to convergence to a value within O( 1/ε √ bN ) of the average of the initial values, with probability at least (1 - b).