90-year-old Bush, a Texas resident, was admitted to Houston Methodist Hospital on Tuesday as a precaution.
His spokesman Jim McGrath said that the 41st president's prognosis was positive and that he remained hospitalised as a precaution.
"President Bush had another terrific day and is in great spirits," McGrath said in an emailed statement.
Bush's wife, Barbara, as well as son Neil and daughter- in-law Maria Bush visited the former president, McGrath said.
"He asked that his sincere wishes for a very Merry Christmas be extended to one and all," McGrath said, adding that Bush will remain at the hospital.
Bush spent seven weeks recuperating and became so ill he was believed at one point to be near death.
The former Republican president suffers from Parkinson's disease and cannot use his legs.
But he celebrated his 90th birthday on June 12 by skydiving in Kennebunkport, Maine, with the Army's Golden Knight parachute team.
Bush, patriarch of one of America's prominent political dynasties, is father to former president George W Bush.
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