Let \(p: \mathbb C^{r+n} = \mathbb C^r \times \mathbb C^n \to \mathbb C^r\) be the natural projection and \(\Omega \subset \mathbb C^r \times \mathbb C^n\) a pseudoconvex domain such that each fiber \(\Omega_t = p^{-1}(t)\), \(t \in p(\Omega)\), is a connected Reinhardt domain. According to Kiselman’s minimum principle it is known that for any plurisubharmonic function \(\varphi: \Omega \to \mathbb R\), which is constant along the orbits of the standard \(\mathbb T^n\)-action on \(\mathbb C^n\), also the function \(\varphi^*: p(\Omega) \to \mathbb R\) defined by \(\varphi^*(t) := \inf_{z \in \Omega_t} \varphi(t, z)\) is plurisubharmonic. In this short note the authors present a new proof of such a principle, which is inspired by Demailly’s method of regularisation of plurisubharmonic functions.