We show that very large surface waves from the 2004 Sumatra-Andaman earthquake (M9.2) triggered deep low-frequency (DLF) seismic tremors beneath Japan over a 500 km wide region. The triggered seismicity was periodically excited, synchronized with the amplitudes and phases of the oscillatory surface waves incident on the region. Periodic excitation implies that the specific phase of the surface waves plays an important role for the triggering. Estimation of stress changes in the source regions showed that the volumetric dilatation larger than ~10-8 was the predominant factor for triggering, thereby strongly supporting the hypothesis that DLF events are caused by processes related to fluid flow.