Neutral current (NC) interactions of atmospheric neutrinos on oxygen form one of the major backgrounds in the search for supernova relic neutrinos with water-based Cherenkov detectors. The NC channel is dominated by neutrino quasi-elastic (NCQE) scattering off nucleons inside $^{16}$O nuclei. In this paper we report the first measurement of NCQE cross section using atmospheric neutrinos at Super-Kamiokande (SK). The measurement used 2,778 live days of SK-IV data with a fiducial volume of 22.5 kiloton water. Within the visible energy window of 7.5-29.5 MeV, we observed $117$ events compared to the expected $71.9$ NCQE signal and $53.1$ background events. Weighted by the atmospheric neutrino spectrum from 160 MeV to 10 GeV, the flux averaged NCQE cross section is measured to be $(1.01pm0.17(text{stat.})^{+0.78}_{-0.30}(text{sys.}))times10^{-38}$ cm$^2$.
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