We propose a k-hop Distributed Prescribed Performance Observer (k-hop DPPO) for state estimation in multi-agent systems. The observer allows each agent to estimate the state of those agents that are 2-hop or more distant by communicating only with 1-hop neighbors, while guaranteeing that transient estimation errors satisfy prescribed performance defined a priori. Furthermore, we demonstrate that if the controller with perfect state knowledge drives the system towards the goal and the estimation based closed-loop system is set-Input to State Stable (set-ISS) with respect to the set describing the goal, then the state estimates can be adapted to achieve the teams objective. Simulation results are provided to demonstrate the effectiveness of the proposed results.