A new pulse-echo interferometry system has been developed for measurements of sound velocity at simultaneous high pressure and temperature corresponding to those of the Earth's lower mantle, using synchrotron X-ray techniques at SPring-8. A combination of a low-noise high-frequency amplifier and a high-speed solid-state relay system allowed us to clearly detect the ultrasonic echoes of a small sample (<1.0 mm in diameter and length) in multi-anvil apparatus. A new high-pressure cell has also been introduced for precise measurement of the length of the tiny sample by X-ray radiography imaging under very high pressure and temperature. The new system was tested by measuring elastic velocities of α-Al2O3 over wide pressure and temperature ranges of up to 27 GPa and 1873 K, respectively. The resultant adiabatic bulk modulus, shear modulus, and pressure and temperature derivatives of α-Al2O3 are K0S = 251.2 (18) GPa, ∂KS/∂P = 4.21 (10), ∂KS/∂T = -0.025 (1), G = 164.1 (7), ∂G/∂P = 1.59 (3), ∂G/∂T = -0.021 (1). These values are consistent with those previously reported based on experiments at high temperatures at ambient pressure and high pressures at room temperature. The present system allows precise measurements of the elastic velocities of minerals under the pressures and temperatures corresponding to the lower mantle for the first time, which should greatly contribute to our understanding of mineralogy of the whole mantle.