  We study the variational structure of the discrete Kadomtsev-Petviashvili
(dKP) equation by means of its pluri-Lagrangian formulation. We consider the
dKP equation and its variational formulation on the cubic lattice ${\mathbb
Z}^{N}$ as well as on the root lattice $Q(A_{N})$. We prove that, on a lattice
of dimension at least four, the corresponding Euler-Lagrange equations are
equivalent to the dKP equation.
