In the near future, cellular machine-to-machine (M2M) communications are expected to play an important role to realize the Internet of Things (IoT). Due to the exponentially growing number of machine nodes, however, one of challenging issues is to accommodate their random access (RA) requests without severely degrading the performance of human-to-human (H2H) communications. In this letter, we propose an enhanced RA scheme with spatial group based reusable preamble allocation (ERA-SGRPA), which reuses the preamble resources based on a spatial grouping during the RA procedure. By allocating the identical preamble set to the groups which are far apart from each other, the ERA-SGRPA scheme enables the given preamble set to be efficiently reused. The performance evaluation shows that the ERA-SGRPA scheme significantly lowers the collision probability and reduces the access delay and can accommodate a significantly larger number of machine nodes without degrading the performance of H2H communications.