In this paper, we propose a novel digital twin scheme supported metaverse by jointly considering the integrated model of communications, computing, and storage through the employment of mobile edge computing (MEC) and ultra-reliable and low latency communications (URLLC). The MEC-based URLLC digital twin architecture is proposed to provide powerful computing infrastructure by exploring task offloading, and task caching techniques in nearby edge servers to reduce the latency. In addition, the proposed digital twin scheme can guarantee stringent requirements of reliability and low latency, which are highly applicable for the future networked systems of metaverse. For this first time in the literature, our paper addresses the optimal problem of the latency/reliablity in digital twins-enabled metaverse by optimising various communication and computation variables, namely, offloading portions, edge caching policies, bandwidth allocation, transmit power, computation resources of user devices and edge servers. The proposed scheme can improve the quality-of-experience of the digital twin in terms of latency and reliability with respect to metaverse applications.