Graham, 88, was in fair condition Monday morning, said Merrell Gregory, a spokeswoman for Mission Health & Hospitals in Asheville.
"His family reports that he's been up and walking, which is excellent," Gregory said. "The family says they see continual improvement."
No date has been set to release Graham, who had some intestinal bleeding Monday morning. The bleeding stopped soon afterward, Gregory said.
"He stayed fully alert, and his condition quickly stabilized," she said.
Family members said they hoped his hospital stay would be brief, but Gregory said he will stay in the hospital for observation while doctors try to find the source of the bleeding and to determine a course for his ongoing care.
The hospital has said the initial bleeding may have been caused by diverticuli, or small pouches that can form in the lower intestine. A diverticular bleed often begins suddenly and may stop on its own, the hospital said.
On Sunday, Graham was able to watch a televised worship service form First Baptist Church of Spartanburg, S.C., and visit with family and friends, hospital officials said.
Graham, who suffers from a variety of ailments including Parkinson's disease and age-related macular degeneration, has been largely confined to his western North Carolina home in recent years.
His wife, Ruth Bell Graham, died in June following a following a lengthy illness.