  In this paper we consider a general class of second order stochastic partial
differential equations on $\mathbb{R}^d$ driven by a Gaussian noise which is
white in time and it has a homogeneous spatial covariance. Using the techniques
of Malliavin calculus we derive the smoothness of the density of the solution
at a fixed number of points $(t,x_1), \dots, (t,x_n)$, $t>0$, assuming some
suitable regularity and non degeneracy assumptions. We also prove that the
density is strictly positive in the interior of the support of the law.
