Context. A recent survey of a large sample of Galactic intermediate-mass (>3 M&sun;) asymptotic giant branch (AGB) stars shows that they exhibit large overabundances of rubidium (Rb) up to 100-1000 times solar. In contrast, zirconium (Zr) is not enriched in these stars compared to its solar abundances. These observations set constraints on our theoretical notion of the slow neutron capture process (s process) that occurs inside intermediate-mass AGB stars. Lithium (Li) abundances are also reported for these stars. In intermediate-mass AGB stars, Li can be produced by proton captures occuring at the base of the convective envelope. For this reason the observations of Rb, Zr, and Li set complementary constraints on different processes occurring in the same stars. Aims: We present predictions for the abundances of Rb, Zr, and Li as computed for the first time simultaneously in intermediate-mass AGB star models and compare them to the current observational constraints. Methods: We calculate the Rb, Zr, and Li surface abundances for stellar models with masses between 3 and 6.5 M&sun; and metallicities between 0.02 and 0.004. Results: We find that the Rb abundance increases with increasing stellar mass, as is inferred from observations but we are unable to match the highest observed [Rb/Fe] abundances. Variations of the reaction rates of the neutron-capture cross sections involved with Rb production and the rate of the 22Ne(α,n)25Mg reaction, responsible for neutron production inside these stars, yield only modest variations in the surface Rb content of ≈0.3 dex. Inclusion of a partial mixing zone (PMZ) to activate the 13C(α,n)16O reaction as an additional neutron source yields significant enhancements in the Rb abundance. However this leads to Zr abundances that exceed the upper limits of the current observational constraints. If the third dredge-up (TDU) efficiency remains as high during the final stages of AGB evolution as during the earlier stages, we can match the lowest values of the observed Rb abundance range. We predict large variations in the Li abundance, which are observed. Finally, the predicted Rb production increases with decreasing metallicity, in qualitative agreement with observations of Magellanic Cloud AGB stars. However stellar models of Z = 0.008 and Z = 0.004 intermediate-mass AGB stars do not produce enough Rb to match the observed abundances.