In cellular networks, Device to Device (D2D) communication can improve spectral efficiency by enabling proximity users to communicate directly without traversing the Base Station (BS). However, if not designed properly, the interference generated by D2D transmissions, may deteriorate the communication quality of the existing cellular and D2D users. In this paper, we study transmission power control-based interference management to increase access rate and sum rate while guaranteeing the Quality of Service (QoS) requirements for both D2D and cellular users. A four-step framework is proposed. First candidate D2D groups, potentially admissible for transmission, are arranged in order with respect to their distance from BS and required Signal to Interference and Noise Ratio (SINR). Next, upper and lower bounds on the transmission power of the transmitters are calculated to determine the admissibility of the aspirant D2D group subject to the QoS requirements of the aspirant group, other scheduled D2D groups, and the cellular user. Then, relay-based communication protocol is considered for admitting the D2D groups that cannot be admitted directly. Finally, sum rate of each shared channel is improved through iterative incrementation of transmission powers of cellular and D2D transmitters constraint by the QoS requirements of all the admitted D2D groups and the cellular user and the existing sum rate. Simulation results show that the proposed framework can improve the access rate many folds across all the considered scenarios as compared to the baseline schemes. Moreover, higher access rates of the proposed scheme translate into significantly higher sum rates.