  Let $M$ be an open Riemann surface and let $\Lambda\subset M$ be a closed
discrete subset. In this paper, we prove the existence of complete conformal
minimal immersions $M\to\mathbb{R}^n$, $n\ge 3$, with prescribed values on
$\Lambda$ and whose generalized Gauss map $M\to\mathbb{CP}^{n-1}$, $n\ge 3$,
avoids $n$ hyperplanes of $\mathbb{CP}^{n-1}$ located in general position. In
case $n=3$, we obtain complete nonflat conformal minimal immersions whose Gauss
map $M\to\mathbb{S}^2$ omits two (antipodal) values of the sphere.
  This result is deduced as a consequence of an interpolation theorem for
conformal minimal immersions $M\to\mathbb{R}^n$ into the Euclidean space
$\mathbb{R}^n$, $n\ge 3$, with $n-2$ prescribed components.
