An annual modulation signal due to the Earth orbiting around the Sun would be one of the strongest indications of the direct detection of dark matter. In 2016, we reported a search for dark matter by looking for this annual modulation with our single-phase liquid xenon XMASS-I detector. That analysis resulted in a slightly negative modulation amplitude at low energy. In this work, we included more than one year of additional data, which more than doubles the exposure to 800 live days with the same 832 kg target mass. When we assume weakly interacting massive particle (WIMP) dark matter elastically scattering on the xenon target, the exclusion upper limit for the WIMP-nucleon cross section was improved by a factor of 2 to 1.9$times$10$^{-41}$cm$^2$ at 8 GeV/c$^2$ at 90% confidence level with our newly implemented data selection through a likelihood method. For the model-independent case, without assuming any specific dark matter model, we obtained more consistency with the null hypothesis than before with a $p$-value of 0.11 in the 1$-$20 keV energy region. This search probed this region with an exposure that was larger than that of DAMA/LIBRA. We also did not find any significant amplitude in the data for periodicity with periods between 50 and 600 days in the energy region between 1 to 6 keV.
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