Temporal clustering of tsunami sources is examined in terms of a branching process model. It previously was observed that there are more short interevent times between consecutive tsunami sources than expected from a stationary Poisson process. The epidemic‐type aftershock sequence (ETAS) branching process model is fitted to tsunami catalog events, using the earthquake magnitude of the causative event from the Centennial and Global Centroid Moment Tensor (CMT) catalogs and tsunami sizes above a completeness level as a mark to indicate that a tsunami was generated. The ETAS parameters are estimated using the maximum‐likelihood method. The interevent distribution associated with the ETAS model provides a better fit to the data than the Poisson model or other temporal clustering models. When tsunamigenic conditions (magnitude threshold, submarine location, dip‐slip mechanism) are applied to the Global CMT catalog, ETAS parameters are obtained that are consistent with those estimated from the tsunami catalog. In particular, the dip‐slip condition appears to result in a near zero magnitude effect for triggered tsunami sources. The overall consistency between results from the tsunami catalog and that from the earthquake catalog under tsunamigenic conditions indicates that ETAS models based on seismicity can provide the structure for understanding patterns of tsunami source occurrence. The fractional rate of triggered tsunami sources on a global basis is approximately 14%.