The effect of an ultrathin Pb film deposited on the surface of Bi₂Se₃ and Sb₂Te₃ compounds on the electronic state structure of topological insulators is studied experimentally by the angle-resolved photoemission spectroscopy (ARPES) technique. The following features are revealed: formation of two-dimensional quantum-well states in the near-surface region, an increase in the binding energy of the Dirac cone and the core levels, and a simultaneous electronic states intensity redistribution in the system in photoemission spectra. The results obtained show that topological states may coexist at the interface between studied materials and a superconductor, which seems to be promising for application in quantum computers.