In this work, we present the first spectroscopic measurements of conversion electrons originating from the decay of metastable gaseous $^mathrm{83m}$Kr with the Karlsruhe Tritium Neutrino (KATRIN) experiment. The results obtained in this calibration measurement represent a major commissioning milestone for the upcoming direct neutrino mass measurement with KATRIN. The successful campaign demonstrates the functionalities of the full KATRIN beamline. The KATRIN main spectrometers excellent energy resolution of ~ 1 eV made it possible to determine the narrow K-32 and L$_3$-32 conversion electron line widths with an unprecedented precision of ~ 1 %.