The increasing number of collective communication-based services with a mass interest and the parallel increasing demand for service quality are paving the way toward end-to-end QoS guarantees. Although many multicast algorithms in interconnection networks have been widely reported in the literature, most of them handle the multicast communication within limited performance metrics, i.e., either delay/latency or throughput. In contrast, this study investigates the multicast communication within a group of QoS constrains, namely latency, jitter, throughput, and additional traffic caused. In this paper, we present the Qualified Groups (QGs) as a novel path-based multicast algorithm for interconnection networks. To the best of our knowledge, the QG is the first multicast algorithm that considers the multicast latency at both the network and node levels across different traffic scenarios in interconnection networks. Our analysis shows that the proposed multicast algorithm exhibits superior performance characteristics over other well-known path-based multicast algorithms under different operating conditions. In addition, our results show that the QG can significantly improve the parallelism of the multicast communication.