"Upon admission, he was alert and in good spirits," said the statement, which was released both by Mission Hospital in Asheville and the The Billy Graham Evangelistic Association.
The 93-year-old was also hospitalized for pneumonia in November. Since then, he has remained "in good overall health ... though he continues to remain at home due to age-related conditions," according to the hospital and association.
The influential preacher went to the hospital for treatment for bronchitis and after developing a "slight fever overnight," his spokesman A. Larry Ross said via Twitter.
He is being treated with oral antibiotics and improving, at one point Sunday even sitting up in bed to remotely watch his grandson Will Graham give a guest sermon at First Baptist Church in Spartanburg, South Carolina, according to the spokesman.
On Sunday, Billy Graham was "resting comfortably" and in stable condition, the hospital and association said in their statement, citing pulmonologist David Pucci at Mission Hospital.
Physicians expect him to remain in the western North Carolina medical facility for four days, according to Ross.
"Doctors are pleased that Billy Graham's condition is much further progressed than for previous hospitalizations for pulmonary infections," Ross wrote, adding that the evangelist was "vibrant, alert and in good spirits with no fever" on Sunday.
Even with his advanced age and health issues, Graham remains "actively involved in ministry and writing projects," his evangelistic association and the hospital said. That includes writing a new book, which is almost done, "summarizing his Gospel message over the past seven decades of public ministry."