According to various estimates, only a small percentage of existing viruses have been discovered, naturally much less being represented in the genomic databases. High-throughput sequencing technologies develop rapidly, empowering large-scale screening of various biological samples for the presence of pathogen-associated nucleotide sequences, but many organisms are yet to be attributed specific loci for identification. This problem particularly impedes viral screening, due to vast heterogeneity in viral genomes. In this paper, we present a new bioinformatic pipeline, VirIdAl, for detecting and identifying viral pathogens in sequencing data. We also demonstrate the utility of the new software by applying it to viral screening of the feces of bats collected in the Moscow region, which revealed a significant variety of viruses associated with bats, insects, plants, and protozoa. The presence of alpha and beta coronavirus reads, including the MERS-like bat virus, deserves a special mention, as it once again indicates that bats are indeed reservoirs for many viral pathogens. In addition, it was shown that alignment-based methods were unable to identify the taxon for a large proportion of reads, and we additionally applied other approaches, showing that they can further reveal the presence of viral agents in sequencing data. However, the incompleteness of viral databases remains a significant problem in the studies of viral diversity, and therefore necessitates the use of combined approaches, including those based on machine learning methods.