Proton-proton and proton-eta invariant mass distributions and the total cross section for the pp to pp eta reaction have been determined near the threshold at an excess energy of Q=10 MeV. The experiment has been conducted using the COSY-11 detector setup and the cooler synchrotron COSY. The determined invariant mass spectra reveal significant enhancements in the region of low proton-proton relative momenta, similarly as observed previously at higher excess energies of Q=15.5 MeV and Q= 40MeV.