  We show the existence of gap-Townes solitons for the multidimensional
Gross-Pitaeviskii equation with attractive interactions and in two- and
three-dimensional optical lattices. In absence of the periodic potential the
solution reduces to the known Townes solitons of the multi-dimensional
nonlinear Schr\"odinger equation, sharing with these the propriety of being
unstable against small norm (number of atoms) variations. We show that in the
presence of the optical lattice the solution separates stable localized
solutions (gap-solitons) from decaying ones, characterizing the delocalizing
transition occurring in the multidimensional case. The link between these
higher dimensional solutions and the ones of one dimensional nonlinear
Schr\"odinger equation with higher order nonlinearities is also discussed.
