Provided are: an engine-mounted controller capable of being suitably used in a vehicle that carries out an idle-stop operation while the vehicle is moving; and a vehicle. An engine-mounted controller of a vehicle determines whether or not an engine is in a completely stopped state when an idle-stop operation is canceled. If the controller determines that the engine is in a completely stopped state, a first control operation for suppressing the transmission of engine vibrations associated with engine idling is executed on the assumption that the engine is in a completely stopped state, and if the controller determines that the engine is not in a completely stopped state, the first control operation is prohibited when the engine restarts.