The electron-phonon interaction in magnesium diboride MgB2 single crystals is investigated by point-contact (PC) spectroscopy. For the first time the electron coupling with E(2g) phonon modes is resolved in the PC spectra. The correlation between intensity of the extremely broad E(2g) modes in the PC spectra and value of the superconducting gap is established. Our observations favor current theoretical models for electron-phonon mediated superconductivity in MgB2, and they better match the harmonic phonon model.