"Even if there is an earthquake of 5.0 or 5.5 on the Richter scale, Florence will stay in one piece. And David would be the last to fall," Marco Ferri, a spokesman for the authority, said.
A study by Italy's National Research Council last week pointed to "a series of micro-fractures on the lower part of both legs" and said this "threatened its stability".
The report said the weaknesses were likely linked to the period between when the statue was completed in 1504 and installed on the Piazza della Signoria and when it was moved to a museum for safekeeping in 1873.
The statue was replaced on the square with a copy.
The study said that the pedestal was at a slight tilt of up to five degrees, putting pressure on the statue.
But Ferri said there was "nothing dramatic about the findings" and the museum would continue monitoring vibrations of the work as it has already been doing.
He said the vibrations have gone down since the number of visitors allowed in at one time is now limited.
Florence's museums had more than five million visitors last year, with many visiting David and the Uffizi Gallery.
"It will not be moved or put on a pneumatic pedestal or anything like that. Apart from anything else, it would be complicated to move a colossus like that," he said.