Lithium and zirconium abundances (the latter taken as representative of s-process enrichment) are determined for a large sample of massive Galactic O-rich AGB stars, for which high-resolution optical spectroscopy has been obtained (R˜ 40 000{-}50 000). This was done by computing synthetic spectra based on classical hydrostatic model atmospheres for cool stars and using extensive line lists. The results are discussed in the framework of "hot bottom burning" (HBB) and nucleosynthesis models. The complete sample is studied for various observational properties such as the position of the stars in the IRAS two-colour diagram ([ 12] - [25] vs. [ 25] - [60] ), Galactic distribution, expansion velocity (derived from the OH maser emission), and period of variability (when available). We conclude that a considerable fraction of these sources are actually massive AGB stars (M>3{-}4 M&sun;) experiencing HBB, as deduced from the strong Li overabundances we found. A comparison of our results with similar studies carried out in the past for the Magellanic Clouds (MCs) reveals that, in contrast to MC AGB stars, our Galactic sample does not show any indication of s-process element enrichment. The differences observed are explained as a consequence of metallicity effects. Finally, we discuss the results obtained in the framework of stellar evolution by comparing our results with the data available in the literature for Galactic post-AGB stars and PNe. Based on observations at the 4.2 m William Herschel Telescope operated on the island of La Palma by the Isaac Newton Group in the Spanish Observatorio del Roque de Los Muchachos of the Instituto de Astrofisica de Canarias. Also based on observations with the ESO 3.6 m telescope at La Silla Observatory (Chile). Tables [see full text]-[see full text] are only available in electronic form at http://www.aanda.org