We study the properties of the light pseudoscalar mesons in a three flavor chiral quark model with nonlocal separable interactions. We concentrate on the evaluation of meson masses and decay constants, considering both the cases of Gaussian and Lorentzian nonlocal regulators. The results are found to be in quite good agreement with the empirical values, in particular in the case of the ratio f_K/f_π and the anomalous decay π⁰ → γ γ. In addition, the model leads to a reasonable description of the observed phenomenology in the η-η′ sector, even though it implies the existence of two significantly different state mixing angles.