  Let $\mathfrak{g}$ be a finite-dimensional complex simple Lie algebra with
highest root $\theta$ and let $\mathfrak{g}[t]$ be the corresponding current
algebra. In this paper, we consider the $\mathfrak{g}[t]$-stable Demazure
modules associated to integrable highest weight representations of the affine
Lie algebra $\widehat{\mathfrak{g}}$. We prove that the fusion product of
Demazure modules of a given level with a single Demazure module of a different
level and with highest weight a multiple of $\theta$ is a generalized Demazure
module, and also give defining relations. This also shows that the fusion
product of such Demazure modules is independent of the chosen parameters. As a
consequence we obtain generators and relations for certain types of generalized
Demazure modules. We also establish a connection with the modules defined by
Chari and Venkatesh.
