In this paper, a single-letter characterization for the capacity region of finite-state multiple access channels (MACs) with partially cooperative encoders is derived. Partial cooperation here is in the sense that the encoders communicate with each other through finite-capacity links. The channel states are assumed to be governed by a Markov processes. Full channel state information (CSI) is assumed at the receiver, while only delayed CSI is available at transmitters. The capacity region is derived by first solving the case of finite-state multiple access channels with common message, using rate splitting, multiplexing and simultaneous decoding in order to establish the achievability. The common message result is then used to derive the capacity region of the partially cooperative encoders case. Finally, we apply this result in order to obtain the capacity region for a finite-state Gaussian MAC with partially cooperative encoders.