A subset $\mathcal{F}$ of a finite transitive group $G\leq \operatorname{Sym}(Ω)$ is intersecting if for any $g,h\in \mathcal{F}$ there exists $ω\in Ω$ such that $ω^g = ω^h$. The \emph{intersection density} $ρ(G)$ of $G$ is the maximum of $\left\{ \frac{|\mathcal{F}|}{|G_ω|} \mid \mathcal{F}\subset G \mbox{ is intersecting} \right\}$, where $G_ω$ is the stabilizer of $ω$ in $G$. In this paper, it is proved that if $G$ is an imprimitive group of degree $pq$, where $p$ and $q$ are distinct odd primes, with at least two systems of imprimitivity then $ρ(G) = 1$. Moreover, if $G$ is primitive of degree $pq$, where $p$ and $q$ are distinct odd primes, then it is proved that $ρ(G) = 1$, whenever the socle of $G$ admits an imprimitive subgroup.