He is in a stable condition at Mission Hospital, in Asheville, North Carolina, where he was admitted on Sunday.
He spent last night in hospital but was reportedly able to watch the closing ceremony of the London Olympics on Sunday evening and eat breakfast on Monday morning.
"Mr Graham continues to do well and the infection is responding well to treatment," said Mission Hospital pulmonologist, David Pucci.
Mr Graham's spokesman, A. Larry Ross, added: "The ceremony brought back fond memories of various crusades Mr Graham held in the UK and in Rio de Janeiro, the host city for the next Summer Olympics, over seven decades of public ministry."
Mr Graham was admitted to hospital early on Sunday morning and was well enough to receive a visit from his daughter, Gigi, and one of his grandchildren.
No date has been set for discharge, but physicians are hopeful that Mr Graham will continue his rapid rate of recovery and return home soon.
Mr Graham had a short spell in hospital last November for the treatment of pneumonia.
He has remained in good health since then, although he spends much of his time at home due to age-related conditions.
He remains actively involved in ministry and writing projects, and is working on a new book summarising his Gospel message over the past seven decades of public ministry.