Veteran environmental broadcaster Attenborough found the fossil during a family vacation in Malta in the late 1960s, Kensington Palace said, and gave it to George last week.
The tooth, which once belonged to a megalodon, is believed to be around 23 million years old.
The gift has raised questions in the Mediterranean nation, prompting Maltese Culture Minister Jose Herrera to say the tooth should be in a local museum and promising to ‘get the ball rolling’ to get it back.
But the government poured cold water on the plan on Tuesday.
Neither the royal family nor representatives for Attenborough have commented on the controversy to CNN.
Many countries now prohibit tourists from removing fossils or seashells from their beaches.
Herrera first told The Times of Malta: “There are some artefacts that are important to Maltese natural heritage and have found their way abroad and are worth recovering”. He did not give details of how he planned to recover the fossil.
“We rightly pay a lot of attention to historical and artistic artefacts. However, this is not always the case with our natural history. I am determined to lead a change in this attitude, ”added the Minister at the time.
CNN’s Amy Cassidy contributed to this report.