The 84-year-old pontiff has not suffered any more breathing spasms, the Holy See said, but he may have to spend up to a week in the hospital to fully recover.
In a further sign that the Pope's health had stabilised, papal spokesman Joaquin Navarro-Valls said the Vatican would not issue another medical bulletin until noon today. The Holy See has said the Pope would spend a few more days at Rome's Gemelli Polyclinic hospital.
"The Pope has rested well" with no repetition of the breathing spasms that sent him to hospital on Tuesday night, Mr Navarro-Valls said. "He rested well all night, and the laboratory tests that were made give a satisfactory result."
Mr Navarro-Valls did not say exactly how long the Pope would remain hospitalised, but he told reporters: "In my personal experience, when I've had the flu, it lasts seven days or a week take your pick."
Vatican officials said the Pope was expected to deliver his weekly address on Sunday from the hospital rather than from his usual perch from a window overlooking St Peter's Square. A hospital spokesman said the Pope was attended by a team of three doctors, including his personal physician, the clinic's emergency department director and an ear, nose and throat specialist.
The Pope is "recovering well", said Cardinal Angelo Sodano, who, as secretary of state, is the Vatican's number two. He said the Pope's breathing problems could have been handled at the Vatican, where the Pope had been laid up since Sunday evening with flu. "But the Holy Father, as everybody, entrusts himself to the doctors," and the decision was made to hospitalise him, he said.