Understanding the origin of ultra-high energy cosmic rays is still a challenge. The average composition as a function of primary energy is a key information to elucidate the origin of these very energetic particles. The most sensitive observables to the mass composition are the atmospheric depth of the shower maximum and the muon content of the showers. In this work, direct measurements of the muon density at 1000 m from the shower axis observed by the Akeno Giant Air Shower Array (AGASA) are analysed. The selected events have zenith angles θ ≤ 36∘ and energies in the range 18.83 ≤ log10(ER/eV) ≤ 19.46. These are compared to the predictions corresponding to proton, iron, and mixed composition scenarios obtained by using the high-energy hadronic interaction models EPOS-LHC, Sibyll2.3c, and QGSJetII-04. A muon deficit in air shower simulations is observed: The muon density obtained from AGASA data is greater than the one obtained in the mixed composition scenario by a factor of 1.49±0.11 (stat)±0.17 (syst), 1.54±0.12 (stat)±0.18 (syst), and 1.66±0.13 (stat)±0.20 (syst) for EPOS-LHC, Sibyll2.3c, and QGSJetII-04, respectively.