At least nine of the 49 bus passengers were being treated at University of New Mexico Hospital.
Where was the bus traveling?
At least seven people were killed, and numerous 49 passengers aboard the Greyhound bus were injured, although authorities couldn't immediately provide an exact count of how many were hurt or their conditions. The driver of the truck sustained injuries that were not life-threatening, the state police said.
Police say a number of bus passengers were transported to hospitals with serious injuries. Almost every person on board was transported to hospital, CBS reported.
"You could tell that people were distressed, screams were coming from the bus", he said.
"It was an awe-inspiring, bad scene", he said.
Chris Jones was headed west on Interstate 40 when he caught his first glimpse of the semi turned over.
Authorities have not said what caused the crash. He did not have any information on the people who were killed, including their ages, genders or where they were from.
"We are fully co-operating with local authorities and will also complete an investigation of our own", Greyhound spokeswoman Crystal Booker said in a statement.
This is not the first deadly crash involving a passenger bus in the state in recent months.
At least seven people were killed in northwestern New Mexico when a tractor-trailer crashed head-on with a almost packed Greyhound bus, officials said.
New Mexico State Police did not say how many people died or how many were injured in Thursday's crash. Nearby was an overturned vehicle and what appeared to be a truck trailer on its side, with contents spilled on the median. It forced the closure of westbound lanes of the interstate and traffic was backing up as travellers were diverted.
Photos on social media showed a truck on its side with the trailer's cargo scattered across the highway, and the Greyhound bus upright, but with its front end obliterated.
The McKinley County Office of Emergency Management set up a phone line for the family members of passengers who are looking for more information. Debris from the semi also littered the area. Ten investigators will arrive in New Mexico on Friday. Officers and rescue workers were on scene but did not provide details about how many people were killed or injured, or what caused the crash.
Officials said they expect the death toll to rise.