The first results of the study of high-energy electron neutrino (ν_{e}) and muon neutrino (ν_{μ}) charged-current interactions in the FASERν emulsion-tungsten detector of the FASER experiment at the LHC are presented. A 128.8 kg subset of the FASERν volume was analyzed after exposure to 9.5 fb^{-1} of sqrt[s]=13.6 TeV pp data. Four (eight) ν_{e} (ν_{μ}) interaction candidate events are observed with a statistical significance of 5.2σ (5.7σ). This is the first direct observation of ν_{e} interactions at a particle collider and includes the highest-energy ν_{e} and ν_{μ} ever detected from an artificial source. The interaction cross section per nucleon σ/E_{ν} is measured over an energy range of 560-1740 GeV (520-1760 GeV) for ν_{e} (ν_{μ}) to be (1.2_{-0.7}^{+0.8})×10^{-38} cm^{2} GeV^{-1} [(0.5±0.2)×10^{-38} cm^{2} GeV^{-1}], consistent with standard model predictions. These are the first measurements of neutrino interaction cross sections in those energy ranges.