The intercalation of silver atoms in the van der Waals gap of the prototypical three-dimensional topological insulator Bi₂Se₃ is studied by means of ab initio total-energy calculations. Two possible intercalation mechanisms are examined: penetration from the terrace under the step and penetration via interstitials and/or vacancies of the surface quintuple layer block. It is shown that the former mechanism is strongly preferred over the latter one due to significant energy gain appearing at the step. According to performed estimations, the room temperature diffusion length of silver atoms reaches ten microns within a couple of minutes both on the surface and within the van der Waals gap, which essentially exceeds a typical distance between steps. These results shed light on the mechanism of intercalation of metal atoms deposited on the Bi₂Se₃ surface.