Abstract Mergers of galaxies are thought to cause significant gas inflows to the inner parsecs, which can activate rapid accretion on to supermassive black holes (SMBHs), giving rise to active galactic nuclei (AGN). During a significant fraction of this process, SMBHs are predicted to be enshrouded by gas and dust. Studying 52 galactic nuclei in infrared-selected local luminous and ultraluminous infrared galaxies in different merger stages in the hard X-ray band, where radiation is less affected by absorption, we find that the amount of material around SMBHs increases during the last phases of the merger. We find that the fraction of Compton-thick (CT, N H ≥ 1024 cm− 2) AGN in late-merger galaxies is higher ($f_{\rm \,CT}=65^{+12}_{-13}{\rm per\, cent}$) than in local hard X-ray selected AGN (f CT = 27 ± 4 per cent), and that obscuration reaches its maximum when the nuclei of the two merging galaxies are at a projected distance of D12 ≃ 0.4–10.8 kpc ($f_{\rm \,CT}=77_{-17}^{+13}{\rm per\, cent}$). We also find that all AGN of our sample in late-merger galaxies have N H > 1023 cm− 2, which implies that the obscuring material covers $95^{+4}_{-8}{\rm per\, cent}$ of the X-ray source. These observations show that the material is most effectively funnelled from the galactic scale to the inner tens of parsecs during the late stages of galaxy mergers, and that the close environment of SMBHs in advanced mergers is richer in gas and dust with respect to that of SMBHs in isolated galaxies, and cannot be explained by the classical AGN unification model in which the torus is responsible for the obscuration.