Angle-resolved photoemission spectroscopy and Auger electron spectroscopy have been applied to study the intercalation process of silver underneath a monolayer of graphite (MG) on Ni(111). The room-temperature deposition of silver on top of MG/Ni(111) system leads to the islands-like growth of Ag on top of the MG. Annealing of the as-deposited system at temperature of 350-450 C results in the intercalation of about 1-2 ML of Ag underneath MG on Ni(111) independently of the thickness of pre-deposited Ag film (3-100 A). The intercalation of Ag is followed by a shift of the graphite-derived valence band states towards energies which are slightly larger than ones characteristic for pristine graphite. This observation is understood in terms of a weakening of chemical bonding between the MG and the substrate in the MG/Ag/Ni(111) system with a small MG/Ni(111) covalent contribution to this interaction.