Whats going on?

After a dead stop,car begins to vibrate at all speeds while gas pedal is depressed.If you release it the vibration stops while car is in motion.Car does not shake when brakes are applied.It doesnt sway left or right.Alignment,tires and tire press are good.No spitting or stalling or hesitating from injectors.Tested for excessive engine movement.Automatic engine shifts smoothly.I believe that it may be the motor mounts but not totaly sold.Please help!