The disputed tooth is believed to be of a megalodon, an extinct giant shark species.
Jose Herrera, the Maltese minister of Culture, wants the tooth back in a museum on his soil.
Attenborough, 94, presented the fossil to Prince George during a private viewing of his new documentary at Kensington Palace.
On Saturday (September 26), the Duke and Duchess of Cambridge shared a few photos on their Instagram account with their kids - Prince George, 6, Princess Charlotte, 5, and Prince Louis, 2 - meeting one of their favourite celebrities: Sir David Attenborough.
The tooth was discovered by Sir David in Malta in the 1960s.
"There are some artefacts that are important to Maltese natural heritage and which ended up overseas and deserve to be retrieved", Herrera told the Times of Malta, without giving details of how he meant to recover the fossil.
Socially distanced in the open air, the Duke of Cambridge and Sir David were offered directors' chairs with their names printed on the back - but in a change of plan they sat in each other's seats.
Herrara added: "We rightly give a lot of attention to historical and artistic artifacts". However, it is not always the case with our natural history.
Asked about the flap, Maltese Prime Minister Robert Abela said "we should avoid creating unnecessary controversies".
Before you dismiss the claim, however, keep in mind that fossils fall under the definition of cultural heritage as a "movable or immovable object of geological importance".
In the pic, Prince William, 38, and Sir David's navy chairs are positioned next to one another, however, as several royal fans have pointed out, upon closer inspection Will's seat looks to be just a few centimetres taller.
Kensington Palace declined to comment.
This includes working together on William's Earthshot Prize, an ambitious global environment project announced last December to combat climate issues.