Engine shuts down if started after a stop

Chevrolet Lumina 97, 3.1L, 110K miles. Always starts OK from cold state, but if I drive to a store, park, shut down the engine, then return and start the engine, it starts and immediately shuts down. When that happens, I have to press the gas pedal a little immediately after turning on the engine, so the engine goes on somewhat increased pace, and then ease the gas pedal gradually back to idle - that it does not shut down.