Prince George and Princess Charlotte also asked the naturalist a few pressing questions.
Sir David was asked by Prince George, 7, "what animal do you think will become extinct next?"
"Well let's hope there won't be any because there's lots of things we can when animals are in danger of extinction. We can protect them," said Sir David.
"Hello David Attenborough, I like spiders. Do you like spiders too?" asked Charlotte, 5.
"I love spiders and I'm so glad you like them, I think they're wonderful things," Sir David replied.
The touching video was was posted on the Kensington Royal Twitter account.
The siblings recently met Sir David after he attended a private viewing of his new environmental documentary with the Duke of Cambridge - held in the palace's grounds.
William and the veteran broadcaster watched A Life On Our Planet, a revealing and powerful first-hand account in which Sir David reflects on both the defining moments of his life as a naturalist and the devastating changes he has witnessed.
The eager questions were preceded by a gift brought by Sir David for Prince George - a 23 million-year-old giant shark tooth.
The Carcharocles megalodon tooth given to George was found by Sir David during a family holiday to Malta in the late 1960s.
It was embedded in the island's soft yellow limestone, which was laid down during the Miocene period some 23 million years ago.
Sir David recently joined Instagram at the age of 94, on September 24 with his first post declaring that saving the planet is a "communications challenge".
After 60 years making television programmes, the documentary maker enlisted his younger colleagues to help him join the social media site.
The children may have learnt their interviewing technique from their father, who interviewed Sir David at the World Economic Forum in Davos, Switzerland, last year, and during the discussion the broadcaster warned that humanity needed to act so that they did not "annihilate part of the natural world".
The environmentalists are also working together on the Duke's Earthshot Prize, an ambitious global environment project announced last December to combat climate issues.
Further details about the prize are expected in the coming weeks.
David Attenborough: A Life On Our Planet, produced by WWF and Silverback Films, premieres in cinemas on Monday and will launch on Netflix on October 4. An accompanying book is published on October 1.
- Telegraph and Daily Mail
