Evangelist Billy Graham resting at North Carolina hospital

(CNN) -- Evangelist Billy Graham is "doing fine" while being treated at a North Carolina hospital for bronchitis, his spokesman said Monday, August 13th.

On Sunday, Graham "rested well during his first night" at Mission Hospital in Asheville, A. Larry Ross wrote in an e-mail.

"He is up having breakfast and doing fine early Monday," Ross wrote.

In a statement released later Monday morning, the hospital said no discharge date had been set, though doctors hope Graham can return home soon.

"Mr. Graham continues to do well and the infection is responding well to treatment," said pulmonologist David Pucci, according to the statement.

Graham, 93, also was hospitalized for pneumonia last November, six months after similarly being admitted to a hospital for the same condition. 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 the Billy Graham Evangelistic Association.

The influential preacher went to the hospital early Sunday for treatment for bronchitis and after developing a "slight fever overnight," 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, Ross later said. Graham had no fever by Sunday morning, Ross said.

"He's made further progress than for previous hospitalizations (for pulmonary infections)," Ross said Sunday night, adding that Graham is "in good hands" and "feels comfortable" at Mission Hospital, where he has previously been treated.

Graham, a resident of Montreat, about 18 miles east of Asheville, has provided counsel to generations of U.S. presidents, beginning with Harry S. Truman, and is the founder of the Billy Graham Evangelistic Association.

The Charlotte native has preached to untold millions over six decades, beginning his missionary work in 1944 when he started speaking at rallies for the Youth for Christ Campus Life ministry. Five years later, Graham was holding crusades in tents in downtown Los Angeles.

Originally scheduled for three weeks, the crusades drew so many followers, they were extended to seven. His "last crusade" in June 2005 drew 230,000 people.

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."

He also has weighed in on hot-button issues of late, including supporting North Carolina's constitutional amendment to ban gay marriage, which voters passed earlier this year, and last month defending the president of the Chick-fil-A restaurant chain for his opposition to same-sex marriage.

Also in July, in a letter released by his organization, Graham leveled deep criticism at the United States. He compared the country to Sodom and Gomorrah, the biblical cities synonymous with sin.

"Self-centered indulgence, pride and a lack of shame over sin are now emblems of the American lifestyle," Graham wrote.

CNN's Greg Botelho contributed to this report.