The pressure distribution of a focused ultrasound source was reconstructed from a measured pressure field on the focal plane using time-reversal. The two-dimensional Fourier transform of the distribution in the time and space domain showed a peak with a finite phase velocity, which corresponds to a mode of waves propagating from the circumference to the center of the transducer similar to Lamb waves. It was numerically confirmed that the propagating waves significantly enhanced the secondary lobe on the near side of the main focal lobe. The near side lobe was markedly reduced by increasing the thickness of the transducer by three times in the experiment. This significant change is consistent with the hypothesis that the near side lobe was formed by Lamb-like waves.