The search was scaled back overnight, but officers kept a perimeter around the rugged canyon where the gunman is believed to be hiding.
Authorities said 34-year-old Brody Young, a park ranger, was shot three times Friday after stopping a car at Poison Spider Mesa Trail, a popular trailhead. After Young stopped the car, gunfire was exchanged between him and the driver, officials said. Young was reportedly shot in the arm, leg and stomach area.
That suspect's silver Pontiac Grand Am was later found abandoned, about eight miles southwest of the shooting site.
Searchers say they're closing in.
In addition to the car, officers also found a rifle, a backpack and a bloody T-shirt belonging to the gunman.
The ranger is in critical but stable condition in a Colorado hospital.
The Associated Press contributed to this report.