  It was found that $NN$ potential could influence the results of the
quasi-bound state search in the $K^- d$ system, where the corresponding pole is
situated close to the threshold. Three-body Faddeev-type calculations of the
$\bar{K}NN - \pi \Sigma N$ system performed with a new model of nucleon-nucleon
interaction predict the existence of the quasi-bound $K^- d$ state caused by
strong interactions. Its binding energy is small ($1-2$ MeV), while the width
is comparable with the width of the $K^- pp$ quasi-bound state ($40-60$ MeV).
