Kate Middleton, 39, was asked about her new niece during a visit to a school in Cornwall for the G7 summit.
She said: ‘I wish her all the very best, I can’t wait to meet her. We haven’t met her yet but hopefully that will be soon’.
The Duchess also confirmed that she hadn’t had the chance to Facetime with her niece yet, after Harry and Meghan introduced their daughter to the Queen on a video call.
Lilibet Diana Mountbatten-Windsor was born last Friday at Santa Barbara Cottage Hospital, California, weighing 7lb 11 oz.
She will be known as ‘Lili’ for short, after the Royal Family’s nickname for the Queen.
Her middle name was chosen to honour her late grandmother, Diana, Princess of Wales.
It follows months of tensions between the Sussexes and the rest of the Royal Family in the fallout of their explosive interview with Oprah Winfrey.
The couple made a number of shocking claims during the CBS special in March, including that a member of the family raised concerns over what colour their son Archie’s skin would be.
Meghan, 39, said she had suicidal thoughts as she struggled with the pressure of being a senior royal, claiming she couldn’t get any help from Buckingham Palace.
She also said the palace didn’t help her shut down rumours that she made Kate cry during a bridesmaid dress fitting and claimed it had actually been the other way around.
It has been suggested that Harry and Meghan’s choice of name for their newborn daughter could be an ‘olive branch’ to the Royal Family.
The couple have hit back at claims that they did not mention to the Queen in advance what they planned to name their baby, despite a palace source telling the BBC otherwise.
The Duke says he told the Queen they wanted to name their daughter Lilibet and said ‘had she not been supportive, they would not have used the name’.
But it is thought this call was made after the baby was born but before the Sussexes’ announcement.
Rather than backing their turn of events, Buckingham Palace has refused to deny suggestions the Queen was ‘never asked’ about the name.
Reports suggest that while the monarch was told that Lilibet would be named after her, royal aides only found out about her birth with the rest of the world.
Buckingham Palace appeared to be caught off guard by the timing of the news, with a spokesman congratulating the couple 90 minutes after it broke.
Some time after the Sussexes statement but before they responded, the palace posted news about Princess Anne travelling to Dorset for the anniversary of the 13th Signal Regiment.
They finally released a message hailing the ‘happy news’ at 6.34pm