  Basing upon experience from performing double-dimensional reduction of the
D=11 supermembrane on AdS_4 x S^7 background to Type IIA superstring on AdS_4 x
CP^3 we introduce Kaluza-Klein (partial) kappa-symmetry gauge as a vanishing
condition of the contribution to the D=11 supervielbein components tangent to
D=10 space-time proportional to the differential of the coordinate
parametrizing compact 11-th space-time dimension, that is identified with the
supermembrane world-volume compact dimension. For AdS_4 x S^7 supermembrane
Kaluza-Klein gauge removes half Grassmann coordinates associated with 8
space-time supersymmetries, broken by the AdS_4 x CP^3 superbackground, by
imposing D=3 (anti-)Majorana condition on them. The consideration relies on the
realization of osp(4|8) isometry superalgebra of the AdS_4 x S^7
superbackground as D=3 N=8 superconformal algebra. Requiring further vanishing
of the D=10 dilaton leaves in the sector of broken supersymmetries just two
Grassmann coordinates organized into D=3 (anti-)Majorana spinor that defines
minimal SL(2,R)-covariant extension of the OSp(4|6)/(SO(1,3)x U(3))
sigma-model. Among 4 possibilities of such a minimal extension we consider in
detail one, that corresponds to picking out D=3 Majorana coordinate related to
broken Poincare supersymmetry, and show that the AdS_4 x CP^3 superstring
equations of motion in this partial kappa-symmetry gauge are integrable. Also
the relation between the OSp(4|6)/(SO(1,3) x U(3)) sigma-model and the AdS_4 x
CP^3 superstring is revisited.
