We study spatial behavior of heavily excited excitons localized at a two-dimensional space of a specific stacking fault interface in a layered crystal ${\mathrm{BiI}}_{3}.$ Pump-and-probe absorption and resonant luminescence spectra of the exciton states were measured with an intense nanosecond laser not only at the exciting laser spot but at distant points from the exciting spot by applying space-resolved spectroscopy methods. The blueshift proportional to the exciton density was clearly observed on the probe absorption spectra even at the distant points due to high-density excitons flowing out from the exciting spot. The resonant luminescence also shows the spectral change and anomalous spatial expansion depending on the excitation density. The spatial distributions of the energy shift on the probe absorption and the luminescence intensity were analyzed on the basis of a two-dimensional exciton-flow model with dissipation processes. The analysis suggests the existence of an efficient in-phase motion of the exciton polaritons at high density. The results are discussed in terms of a new phase of the interacting high-density exciton-polariton system.