The successful formation of stationary light pulses in a cold atomic medium was demonstrated recently. However, unlike in hot media, a detuning between the counterpropagating fields had to be applied. Here we demonstrate that a significant nonuniform phase variation can be induced during a period of stationary light owing to off-resonantly driven transitions. The experimental results are in good agreement with theoretical predictions for media of low optical depth. For media of high optical depth the numerical simulations indicate that such phase variation becomes negligible. Thus stationary light based on this coupling scheme could be used for possible future applications in quantum information processing.