"We're urging the public to stay vigilant. He's very dangerous and anybody who comes in contact with him is definitely at risk," police Sgt. Robert Eberling said.
Area schools remain on "soft lockdown" as the search for Morales continued, The Dallas Morning News reported.
Morales may still be in the handcuffs and shackles he was wearing when he escaped Monday night, investigators said Tuesday. His chains were not found near the Dallas-area Walmart where he stabbed a Florida police officer and fled, newspaper reported.
Morales, 42, a violent sex offender, was being returned to Nevada from Florida to serve a sentence of 30 years to life. He had been transferred to Florida for legal proceedings that added another 10-year prison term to be served if he is ever released by Nevada.
"This is an extremely dangerous individual, and he's capable of anything," Eberling said Tuesday. "If anyone knows of co-workers in Grapevine who didn't show up to work today, we want to hear about it."
Two Miami police officers escorted Morales to Houston by plane. Investigators said he began hitting his head on the seat in front of him and after the plane landed the airline said he could not fly the next leg of the trip.
The officers decided to continue to Carson City, Nev., in a rented sport utility vehicle and arranged for a third officer to fly to Dallas to join them. On their way to Dallas/Fort Worth International Airport, they visited the Walmart in Grapevine, where one officer went into the store.
Morales, with his hands shackled to a belly chain, somehow managed to stab Miami Detective Jaime Pardinas, 54, after breaking off the earpiece to his glasses. Pardinas remained in serious condition after surgery at Parkland Memorial Hospital.