Let $G$ be a connected reductive algebraic group defined and quasi-split over $\mathbb {R}$. In this paper the Mellin transform of the Whittaker function associated to $G$ is studied. It is shown that this Mellin transform has a meromorphic continuation and satisfies certain explicit difference equations. An effective algorithm for obtaining these difference equations is presented, and is illustrated in low rank cases for $G=\mathrm {GL}(n)$.