Next-generation sequencing based metagenomics has enabled to identify microorganisms in characteristic habitats without the need for lengthy cultivation. Importantly, clinically relevant phenomena such as resistance to medication, virulence or interactions with the environment can vary already within species. Therefore, a major current challenge is to reconstruct individual genomes from the sequencing reads at the level of strains, and not just the level of species. However, strains of one species can differ only by minor amounts of variants, which makes it difficult to distinguish them. Despite considerable recent progress, related approaches have remained fragmentary so far. Here, we present StrainXpress, as a comprehensive solution to the problem of strain aware metagenome assembly from next-generation sequencing reads. In experiments, StrainXpress reconstructs strain-specific genomes from metagenomes that involve up to more than 1000 strains, and proves to successfully deal with poorly covered strains. The amount of reconstructed strain-specific sequence exceeds that of the current state-of-the-art approaches by on average 26.75% across all data sets (first quartile: 18.51%, median: 26.60%, third quartile: 35.05%).