Torus network topology offers many advantages such as higher speed, lower latency, better fairness, and lower energy consumption. For these kinds of benefits, nowadays, it is used to construct many parallel and distributed systems like IBM Blue Gene, IBM Sequoia, Mira, and Sugon TC8600. In parallel and distributed computing, multiple nodes act together to carry out large tasks fast. Hence, coordination is indispensable among these nodes to complete such tasks. A possible coordination method could be to elect a leader among the nodes. Along with coordination, the elected leader node also manages other activities such as task allocation, result aggregation, clock synchronization, proficient resource sharing management, and communication among the system’s nodes. In this paper, we propose a lower bound of message complexity on a comparison-based leader election for a 2D torus network (where N is the number of nodes in the network). Next, we sketch a new leader election algorithm (Lea-TN) considering both the node and link failures for a 2D torus network. This Lea-TN is a deterministic and robust algorithm that elects a leader for a synchronous distributed system. The algorithm chooses a leader, even when there are some link or node failures in the system. We consider the number of non-faulty links and the subsisting nodes’ failure rate to elect a reliable leader. We introduce new patterns for sending messages that help reduce the number of exchanged messages and the execution time of the election process. The proposed algorithm (Lea-TN) enables a node to identify its link failures during the election also. Further, we simulate the Lea-TN algorithm and compare its performance with that of the well-known existing algorithms.