"Oh look, who's this," he says when meeting Luna.
"Hello Luna, you're very sweet Luna."
The footage, which has since gone viral, shows the Prince patting Luna before giving some insight into his pain.
"Dogs at this time are so important," he says. "I give my dog a lot of cuddles at the moment.
"I've got a little spaniel called Orla. She's very sweet."
The dog's owner tells Will: "Sorry for your loss".
"Thank you very much, I appreciate it," he says. "Thank you for coming along today."
In another touching moment, the royal couple beamed after spotting a different dog in the crowd and remarking on the power of pets to comfort during dark times.
"Did you see that doggie as well?" Prince William says while pointing into the crowd in the clip, which quickly went viral.
"Hello, Fergus," he adds, followed by: "Doggies at this time are very important."
Prince William and Kate, the Duchess of Cambridge, had a dog called Lupo — and a spaniel, which died last year.
In a post on social media, the Duke and Duchess wrote: "Very sadly last weekend our dear dog, Lupo, passed away. He has been at the heart of our family for the past nine years and we will miss him so much."
Insiders say William — who is next in line for the throne behind the new monarch King Charles — is embarking on the role with a renewed sense of duty after his devoted grandmother's death.
"The Duke was incredibly close to his grandmother, he looked up to her like no one else," they told the Daily Mail.
"And that service and duty that she epitomised is something that will very much be a characteristic of his future role."
In particular, William has spent time carefully "future-proofing" his charitable empire, the Royal Foundation, ahead of his new appointment, to ensure his major climate change project, the Earthshot Prize, is able to operate independently without his scrupulous involvement.
"He believes that as Prince of Wales he can continue to make a significant contribution, particularly in the area of housing and homelessness," a friend of the 40-year-old said.
"He knows he needs to tread carefully but he won't be silent. He's inherited a lot of his father's campaigning zeal.
"He shares his father's willingness to speak if there's something he believes in for the long term. The Prince of Wales was ridiculed for his views on climate change and look at him now. William wants to bring that to his own work," they said, adding that while the royal doesn't wish to "court controversy" he "is not afraid of taking risks".
