Defining coefficient ring of a cohomology theory

Question

Let $E$ be a ring spectrum with multiplication given by $\mu$. Then we make $E^*(X)$ a module over $E^*(pt)$ as follows. We give a map $$\phi: [S^{-n},E] \times [\Sigma^{-m}X,E] \to [\Sigma^{-m-n}X,E ]$$ The map is just given by $(f,g) \to \mu(f \wedge g)$. Now this makes the cohomology a module over the coefficient ring. Now my question is: Is it necessary that $E$ is a ring spectrum for doing this? Thank you.