Prince Harry and Meghan's baby Lilibet: Kate's sweet message for niece she's yet to meet

Britain's Kate, Duchess of Cambridge, left, and US First Lady Jill Biden laugh during a visit to Connor Downs Academy in Hayle. Photo / AP

The Duchess of Cambridge has revealed that she has not yet been introduced to the Duke and Duchess of Sussex's newborn daughter, Lilibet.

The Duchess was asked about her niece by an American reporter during a visit to a primary school in Cornwall with Jill Biden, the First Lady.

Asked if she had "any wishes" for her niece, she replied: "I wish her the very best. I can't wait to meet her. We haven't met her yet, I hope that will be soon".

Asked if they had FaceTimed, she replied: "No I haven't."

The Duchess of Cambridge with America's First Lady Jill Biden in Cornwall.

The revelation suggests that relations between the Sussexes and the Cambridges remain frosty.

Lilibet Diana Mountbatten-Windsor was born last Friday at a hospital in Santa Barbara, California.

But the Sussexes' decision to use the Queen's highly-personal pet name for their second child has already sparked a row.

Lawyers instructed by Harry and Meghan said it was "false and defamatory" for the BBC to suggest the couple did not ask Her Majesty if they could use the name.

The Duke and Duchess claimed they would not have used the name if the Queen had not been "supportive" of their choice.

Harry and Meghan said they would not have used the name Lilibet if the Queen had not been "supportive" of their choice. Photo / File

But rather than confirming the Duke and Duchess's version of events, the Palace refused to deny suggestions that the Queen was "never asked".

The Daily Telegraph understands the Queen was "told" about the name after the baby was born last Friday, rather than her permission being sought in advance.

It suggests that if the Duke and Duchess chose the name to curry favour with the Queen and the wider Royal family, the tactic has backfired badly.

A spokeswoman for the Sussexes declined to comment.