In this study, collective excitations of liquid indium are studied just above the melting point at different pressures (1.7 GPa, 240 C; 3.0 GPa, 300 C; 4.0 GPa, 360 C). The pressures and temperatures are achieved by the use of an externally heated diamond anvil cell. Clear evidence for the existence of propagating modes is observed from the dynamical structure factor at constant momentum transfer (Q) up to about 18 1/nm. The reason for the observed high elastic-scattering background is identified, and its effects on the determination of elastic properties such as viscosity are discussed.