Atmospheric muons are the dominant component of the down-going events for the KM3NeT neutrino telescopes. Deep underwater measurements of muons provide important information about the cosmic ray properties. The KM3NeT research infrastructure includes two telescopes currently in operation while still being under construction in the Mediterranean Sea. The KM3NeT/ORCA detector is deployed at 2450 m depth near Toulon, France. The KM3NeT/ARCA telescope is located at 3500 m depth off-shore Capo Passero, Italy. In this work, the measured atmospheric muon flux is compared to the Monte Carlo simulation using the CORSIKA package with the Sibyll 2.3d model for high-energy hadronic interactions and the GSF model for mass composition. The data from both KM3NeT/ORCA and KM3NeT/ARCA telescopes are considered for this analysis. In the current configuration, KM3NeT/ORCA covers cosmic ray energy range from several TeV up to hundreds of TeV per nucleon, while for KM3NeT/ARCA the range is from several TeV up to PeV per nucleon. Systematic uncertainties considered for the analysis include that on the cosmic ray flux normalization and its composition, water properties, detector response, and high-energy hadronic interaction models.