The inference of disease transmission networks is an important problem in epidemiology. One popular approach for building transmission networks is to reconstruct a phylogenetic tree using sequences from disease strains sampled from infected hosts and infer transmissions based on this tree. However, most existing phylogenetic approaches for transmission network inference are highly computationally intensive and cannot take within-host strain diversity into account. Here, we introduce a new phylogenetic approach for inferring transmission networks, TNet, that addresses these limitations. TNet uses multiple strain sequences from each sampled host to infer transmissions and is simpler and more accurate than existing approaches. Furthermore, TNet is highly scalable and able to distinguish between ambiguous and unambiguous transmission inferences. We evaluated TNet on a large collection of 560 simulated transmission networks of various sizes and diverse host, sequence, and transmission characteristics, as well as on 10 real transmission datasets with known transmission histories. Our results show that TNet outperforms two other recently developed methods, phyloscanner and SharpTNI, that also consider within-host strain diversity. We also applied TNet to a large collection of SARS-CoV-2 genomes sampled from infected individuals in many countries around the world, demonstrating how our inference framework can be adapted to accurately infer geographical transmission networks. TNet is freely available from https://compbio.engr.uconn.edu/software/TNet/.