  The symmetry of the theory of relativity under diffeomorphisms strongly
depends on the equivalence principle. Violation of Equivalence Principle (VEP)
can be tested by looking for deviations from the standard framework of neutrino
oscillations. In recent works, it has been shown that strong constraints on the
VEP parameter space can be placed by means of the atmospheric neutrinos
observed by the IceCube neutrino telescope. In this paper, we focus on the
KM3NeT neutrino telescope and perform a forecast analysis to assess its
capacity to probe VEP. Most importantly, we examine the crucial role played by
systematic uncertainties affecting the neutrino observations. We find that
KM3NeT will constrain VEP parameters times the local gravitational potential at
the level of $10^{-27}$. Due to the systematic-dominated regime, independent
analyses from different neutrino telescopes are fundamental for robustly
testing the equivalence principle.
