Bush, 88, was admitted to Methodist Hospital on Nov. 23 for bronchitis. He was transferred to intensive care on Sunday after setbacks including a persistent fever.
"President Bush remains in the intensive care unit at Methodist Hospital, where he continues to improve," family spokesman Jim McGrath said in a statement. "The president is alert and, as always, in good spirits -- and his exchanges with doctors and nurses now include singing."
Bush has lower-body parkinsonism, which causes a loss of balance, and has used a wheelchair for more than a year.
Bush was the 41st U.S. president and is the father of former President George W. Bush. In a political career spanning four decades, Bush, a Republican, also served as a congressman, ambassador to the United Nations, envoy to China, CIA director, and vice president for two terms under Ronald Reagan.