The injured man, who was showing signs of a severe head injury, and his climbing partner were stuck for a second night on a 45-degree slope with steep and rocky terrain above and below them. Temperatures dipped below zero Fahrenheit Sunday night.
"There couldn't be a worse place on the mountain to try to do a rescue, it's very extreme terrain," Lee Taylor, a spokeswoman for Mount Rainier National Park.
Peter Cooley, 39, slipped and fell early Saturday morning on Liberty Ridge at the 12,300-foot level of the 14,410-foot mountain.
"He's in and out of consciousness, not coherent, agitated. He's not in good mental condition," Taylor said. She said the injury is life-threatening and he needs to reach a hospital as soon as possible.
His climbing partner, Scott Richards, 42, set up a tent and boiled water, Taylor said. The pair, both from Cape Elizabeth, Maine, had enough supplies to get them through the night as they awaited a rescue effort expected to take several days. The stranded men were in intermittent contact with rescuers by cell phone.
Two rescue climbers started their ascent Saturday and had been expected to reach the stranded men by mid-afternoon. By early Sunday evening, however, they remained more than 3,000 feet below the men and were not expected to get to them until Monday morning, said park spokeswoman Patti Wold.
In the meantime, authorities were able to drop some supplies to the pair, park spokesman Kevin Bacher told CBS Radio News, including an extra sleeping bag and a better radio with which to communicate with rescuers.
Poor weather also prevented an attempt to rescue the stranded men using a helicopter from the Oregon Air National Guard. It was sent to wait back in Yakima, east of the mountain, Wold said.
The rescue climbers planned to figure out how to safely bring down the men once they assessed the situation, Taylor said.
Richards was described as an experienced climber who has scaled the summit before.
Mount Rainier, about 60 miles southeast of Seattle in the Cascade range, is a popular destination for hikers and mountaineers.