Timing advance (TA) estimation at the base station (BS) and reliable decoding of random access response (RAR) at the users are important steps in the initial random access (RA) procedure. However, due to limited availability of physical resources dedicated for RA, successful completion of RA requests would become difficult in high user density scenarios, due to contention among users requesting RA. In this paper, we propose to use the large antenna array at the massive multiple input multiple output BS to jointly group RA requests from different users using the same RA preamble. We then beamform the common RAR of each detected user group onto the same frequency resource, in such a way that most users in the group can reliably decode the RAR. The proposed RAR beamforming therefore automatically resolves the problem of collision between multiple RA requests on the same preamble, which reduces the RA latency significantly as compared to LTE. Analysis and simulations also reveal that for a fixed desired signal-to-interference-and-noise ratio of the received RAR, both the required per-user preamble transmission power and the total RAR beamforming power can be decreased roughly by 1.5 dB with every doubling in the number of BS antennas.