Aeromexico says it involved an Embraer 190 plane with capacity of 100 passengers.
There were 97 passengers and four crew members aboard the Embraer 190 plane, Mexico's Secretary of Communications and Transportation Gerardo Ruiz Esparza wrote on Twitter.
Conesa thanked the crew "for their professionalism" and said that the aircraft "was perfectly maintained", but did not provide details on the circumstances of the accident.
The plane then skidded off the runway at the Guadalupe Victoria International Airport until it stopped about 300 meters away.
Alejandro Cardoza, a spokesman for the state's civil protection agency, said in an interview that around 85 people had suffered mostly light injuries and that the fire had been put out.
Embraer said in a statement that a team of its technicians has been deployed to the scene of the accident in Durango.
The plane reportedly tried to take off in heavy rain before being forced to make an emergency landing.
Aeromexico said there were 88 adult passengers, nine minors, two infants, two pilots and two flight attendants on board the almost full E190, and confirmed that it had no information of human losses.
Earlier, the governor of Durango state said no deaths were recorded.
Officials and witnesses differ on whether the plane either fell shortly after takeoff or ran off the runway without really gaining altitude. Israel Solano Mejia says that "the majority of passengers left (the plane) under their own power".
According to Governor of the State of Durango José Rosas Aispuro Torres, there were no deaths in the accident. He said he didn't know if it was a lightning bolt or a mechanical problem and that they had just taken off when the plane fell. An internet site on the aviation industry said the aircraft was about a decade old. Ambulances lined up at the accident site to ferry the injured to local hospitals.
Aeromexico's Flight 2431 was en route from Durango to Mexico City when it went suddenly started falling, moments after taking off. Passengers were seen walking to a nearby highway to obtain help.