Power is a rate, so it requires a time element. Power is equal to the product of torque and speed (time function). Since speed in an induction motor is a function of the power line frequency, it doesn't change as voltage changes. So power is proportional to torque.
However, I'd like to take exception to one thing that RB said. The impedance of the motor windings is a function of load, speed, and slip. As long as the speed, load, and slip are constant, impedance is constant. So lowering the applied voltage does lower the current.
*But* an induction electric motor tries to compensate for this when available power falls below load demand by increasing slip.As slip increases, the winding impedance falls, and current can increase, even at a lower supply voltage. Increased current yields increased torque, and at the same speed, increased power.
The fly in this ointment is that winding *resistance* doesn't change. Energy dissipated in the windings is a function of the square of current and the winding resistance (P=I^2 * R). So the windings heat more rapidly at a lower line voltage, but speed is constant, so the amount of cooling air remains constant. That causes winding temperature to rise, leading ultimately to insulation failure, and all the magic smoke is let out of the motor.
Gary