The resonant absorption of solar axions by ⁵⁷Fe nuclei, which is accompanied by the excitation of the first excited nuclear level: A + ⁵⁷Fe → ⁵⁷Fe*→ ⁵⁷Fe + γ(14.4 keV), is sought. To seek 14.4-keV photons, a Si(Li) detector and an enriched ⁵⁷Fe target are used. The detector and target are placed in a low-background setup equipped with passive and active shieldings. As a result, a new upper limit m _A ≤ 360 eV (at 90% C.L.) has been determined for the axion mass.