The young royal was given the fossilised tooth from an extinct Carcharocles megalodon when Sir David visited Kensington Palace last week.
The 94-year-old naturist found the tooth during a family holiday to Malta in the late 1960s.
But after George was pictured with the tooth, Jose Herrera, Malta’s culture minister, suggested that he would be asking for it to be handed back to the country.
Now the giant shark tooth will remain with the seven-year-old prince after an apparent climbdown from Malta.
Asked about the issue, prime minister Robert Abela said “we should avoid creating unnecessary controversies”.
A spokeswoman for the culture minister said: “Further to the initial remarks as reported in the Maltese media, minister Herrera would like to reiterate that no action was initiated or will be taken on the issue in (question).”
The Maltese government faced criticism on social media over Mr Herrera’s decision, reported by the Times of Malta, to begin the process of retrieving the tooth from the UK.
The son of murdered anti-corruption journalist Daphne Caruana Galizia, who was killed in a car bombing in 2017, tweeted that Malta’s administration should be focusing on more important issues.
Matthew Caruana Galizia said: “A megalodon tooth costs $40 on eBay. Corruption has cost us billions of euros. I ask my government to prioritise and please get a grip on what’s important.”
Sir David found the tooth embedded in Malta’s soft yellow limestone, which was laid down during the Miocene period some 23 million years ago.
Thousands of examples of the tooth can be found on online auction sites for prices ranging from a few pounds to thousands, although their origins are not always listed.