Images of the crash showed debris strewn across the highway as one of the buses appeared to have hit the back of the other.
Firefighters had to cut one person out of the upper deck and some of injured people were taken to hospital by another bus.
Nine road ambulances, an air ambulance and two response vehicles got to the scene at about 08.34 GMT and also transported some of the injured to hospital, North West Ambulance Service said.
Mr Vaughan said: “Saturday’s collision was a serious one and our thoughts remain with all involved, in particular those who were injured.
“We have asked the operator to carry out an urgent investigation, and once we understand exactly what happened we will work with them to see what steps are needed to ensure our networks continue to operate as safely as possible.
“We will share any relevant updates when we have them.”
