Greyhound said there were 49 passengers on board when the crash happened.
The crash shut down the westbound lanes of Interstate 40 near Thoreau near mile marker 50, police said. Wilson said six people suffered minor injuries; the rest were taken to hospitals.
Police said late Thursday afternoon that at least seven people had died, but investigators expected the number of fatalities to rise.
An investigative team from the National Transportation Safety Board was reportedly en route to the scene.
Part of the side of the bus was torn off, he said.
"I was really traumatised myself, because I've been driving about two years and I had never seen anything like that before", Mr Soto said.
At least seven people have been killed and dozens injured as a lorry crashed head-on into a Greyhound bus in the US.
Wilson said the preliminary investigation found that the truck was heading east when a tire blew out, causing it to cross the median and head into oncoming traffic.
"It was terrible, there was people trying to climb out of the windows of the bus. bystanders trying to help people getting ladders out of their truck to get to windows of Greyhound bus to assist", a witness told KRQE.
The wreckage included a Greyhound bus with front-end damage and a semi-truck that was on its side and with its cargo strewn across the highway and the median.
The crash occurred near the town of Thoreau.
Passing motorists on Interstate 40 described coming upon the harrowing scene, with victims struggling to pull themselves from the mangled bus.
"Our first priority is taking care of our passengers and their families as this incident has deeply impacted all involved", the company said.