Mobile networks have a great challenge by serving the expected billions of Internet of Things (IoT) devices in the upcoming years. Due to the limited simultaneous access in the mobile networks, the devices should compete between each other for resource allocation during a Random-Access procedure. This contention provokes a non-depreciable delay during the device’s registration because of the great number of collisions experienced. To overcome such a problem, a framework called Random-Access Accelerator (RAA) is proposed in this work, in order to speed up network access in massive Machine Type Communication (mMTC). RAA exploits Device-To-Device (D2D) communications, where devices with already assigned resources act like relays for the rest of devices trying to gain access in the network. The simulation results show an acceleration in the registration procedure of 99%, and a freed space of the allocated spectrum until 74% in comparison with the conventional Random-Access procedure. Besides, it preserves the same device’s energy consumption compared with legacy networks by using a custom version of Bluetooth as a wireless technology for D2D communications. The proposed framework can be taken into account for the standardization of mMTC in Fifth-Generation-New Radio (5G NR).