  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
$(1.01\pm0.17(\text{stat.})^{+0.78}_{-0.30}(\text{sys.}))\times10^{-38}$
cm$^2$.
