This paper presents a new multicast path-based algorithm, referred to here as the Qualified Groups (QG for short), which can achieve a high degree of parallelism and low communication latency over a wide range of traffic loads in the mesh. The QG algorithm relies on a new approach that divides the destinations in a way that balances the traffic load on network channels during the propagation of the multicast message. Results from extensive simulations under a variety of working conditions confirm that the QG algorithm exhibits superior performance characteristics over those of some well-known existing algorithms, such as dual-path, multiple-path, and column-path algorithms.