We report on the light sterile neutrino search from the first four-week science run of the KATRIN experiment in 2019. Beta-decay electrons from a high-purity gaseous molecular tritium source are analyzed by a high-resolution MAC-E filter down to 40 eV below the endpoint at 18.57 keV. We consider the framework with three active neutrinos and one sterile neutrino. The analysis is sensitive to the mass, m(4), of the fourth mass state for m(4)(2) less than or similar to 1000 eV(2) and to active-to-sterile neutrino mixing down to vertical bar U-e4 vertical bar greater than or similar to 2 x 10(-2). No significant spectral distortion is observed and exclusion bounds on the sterile mass and mixing are reported. These new limits supersede the Mainz results for m(4)(2) less than or similar to 1000 eV(2) and improve the Troitsk bound for m(4)(2) < 30 eV(2). The reactor and gallium anomalies are constrained for 100 < Delta m(41)(2) < 1000 eV(2).
