  The complete NNLO QCD corrections to the total cross section $\sigma(e^+e^-
\to Z*,\gamma*\to t\bar t)$ in the kinematic region close to the top-antitop
threshold are calculated by solving the corresponding Schroedinger equations
exactly in momentum space in a consistent momentum cutoff regularization
scheme. The corrections coming from the same NNLO QCD effects to the top quark
three-momentum distribution $d\sigma/d |\vec k_t|$ are determined. We discuss
the origin of the large NNLO corrections to the peak position and the
normalization of the total cross section observed in previous works and propose
a new top mass definition, the 1S mass M_1S, which stabilizes the peak in the
total cross section. If the influence of beamstrahlung and initial state
radiation on the mass determination is small, a theoretical uncertainty on the
1S top mass measurement of 200 MeV from the total cross section at the linear
collider seems possible. We discuss how well the 1S mass can be related to the
$\bar{MS}$ mass. We propose a consistent way to implement the top quark width
at NNLO by including electroweak effects into the NRQCD matching coefficients,
which then can become complex.
