The behavior of the non-perturbative parts of the isovector-vector and isovector and isosinglet axial-vector correlators at Euclidean momenta is studied in the framework of a covariant chiral quark model with non-local quark-quark interactions. The gauge covariance is ensured with the help of the P-exponents, with the corresponding modification of the quark-current interaction vertices taken into account. The low- and high-momentum behavior of the correlators is compared with the chiral perturbation theory and with the QCD operator product expansion, respectively. The V-A combination of the correlators obtained in the model reproduces quantitatively the ALEPH and OPAL data on hadronic \(\tau \) decays, transformed into the Euclidean domain via dispersion relations. The predictions for the electromagnetic \( {\rm\pi}^{\pm}- {\rm\pi}^{0}\) mass difference and for the pion electric polarizability are also in agreement with the experimental values. The topological susceptibility of the vacuum is evaluated as a function of the momentum, and its first moment is predicted to be \( {\rm\chi}^{\prime}(0)\approx (50 \mathrm{MeV})^{2}\). In addition, the fulfillment of the Crewther theorem is demonstrated.