For an ideal permanent-magnet DC motor the voltage controls the speed and the torque controls the current. Real motors aren't ideal - as you increase the load the resistance of the windings causes IR losses and the voltage drop means the speed decreases from the ideal. The working torque will probably be the same as this is limited by the current in the windings and the thermal considerations. For really low supply voltages the stall torque will be less then the normal working torque at the nominal voltage.
Good motors come with datasheets that show the current and torque curve for the motor.
BTW for a series- or shunt-wound motor with field windings ignore the above.