We searched for resonant excitation of the first excited state of the ¹⁶⁹Tm nucleus by axions formed inside the Sun by the Primakoff effect, A + ¹⁶⁹Tm → ¹⁶⁹Tm* → ¹⁶⁹Tm + γ (8.41keV). Gamma quanta with an energy of 8.41keV were registered by a sectionalized Si(Li) detector installed in a low-background setup. As a result, we set a new upper limit for the photon to axion coupling constant, g_Aγ(GeV^-1)m_A(eV) ≤ 1.06 × 10^-5, which for a hadronic axion model corresponds to a mass limit of m_A ≤ 169 eV at a 90% confidence level.