Mergers of galaxies are an important mode for galaxy evolution because they serve as an efficient trigger of powerful starbursts. However, observational studies of molecular gas properties during their early stages are scarce. We present interferometric CO(2-1) maps of two luminous infrared galaxies, NGC 3110 and NGC 232, obtained with the Submillimeter Array with ∼1 kpc resolution. While NGC 3110 is a spiral galaxy interacting with a minor (14:1 stellar mass) companion, NGC 232 is interacting with a similarly sized object. We find that such interactions in these galaxies have likely induced enhancements in the molecular gas content and central concentrations, partly at the expense of atomic gas. The obtained molecular gas surface densities in their circumnuclear regions are Σmol102.5 M o pc-2, higher than in noninteracting objects by an order of magnitude. Gas depletion times of 0.5-1 Gyr are found for the different regions, lying in between noninteracting disk galaxies and the starburst sequence. In the case of NGC 3110, the spiral arms show on average 0.5 dex shorter depletion times than in the circumnuclear regions if we assume a similar H2-CO conversion factor. We show that even in the early stages of the interaction with a minor companion, a starburst is formed along the circumnuclear region and spiral arms, where a large population of SSCs is found (∼350), and at the same time a large central gas concentration is building up that might be the fuel for an active galactic nucleus. The main morphological properties of the NGC 3110 system are reproduced by our numerical simulations and allow us to estimate that the current epoch of the interaction is at ∼150 Myr after closest approach.