The search for resonant absorption of the Primakoff solar axions by ¹⁶⁹Tm nuclei have been performed. Such an absorption should lead to the excitation of low-lying nuclear energy level: A + ¹⁶⁹Tm → ¹⁶⁹Tm^* → ¹⁶⁹Tm + γ (8.41 keV). The Si(Li) detector and ¹⁶⁹Tm target placed inside the low-background setup were used for that purpose. As a result, a new restriction on the axion-photon coupling and axion mass was obtained: g_{A γ} (GeV^{- 1}) ṡ m_A (eV) ≤ 1.36 × 10^{- 5} (90% c.l.). In model of hadronic axion this restriction corresponds to the upper limit on axion mass - m_A ≤ 191 eV for 90% c.l.