Kate Middleton spoke of her niece Lilibet "Lili" Diana for the first time during an engagement on Friday, and said she can't wait to meet the newborn.

The Duchess of Cambridge revealed that she hasn't yet had the chance to see her week-old niece, the second child of her brother-in-law Prince Harry and sister-in-law Meghan Markle. "I wish her all the very best. I can't wait to meet her. We haven't met her yet. I hope that will be soon," she said.

The 39-year-old made the comments while visiting a school in Cornwall with United States first lady Jill Biden, who was in the UK for the G7 summit. When asked whether she had FaceTimed Lili who is in Santa Barbara, California, the Duchess replied, "No, I haven't."

Kate and her husband Prince William had previously congratulated the Sussexes when they announced Lili's arrival on June 6, two days after she was born. The Cambridges wrote on their social media accounts alongside a picture Meghan and Harry had released in February to announce their pregnancy: "We are all delighted by the happy news of the arrival of baby Lili. Congratulations to Harry, Meghan and Archie."

A source told Us Weekly that the parents of three were "informed about the birth and have sent Lilibet a gift."

The relationship between the Cambridges and the Sussexes, particularly Princes William and Harry, has been strained since even before the latter announced his exit from the royal family. The Duke of Sussex had explained his rift with his only sibling in his and Meghan's tell-all with Oprah Winfrey in March.

"I love William to bits. We've been through hell together and we have a shared experience, but we are on different paths," the 36-year-old said about his elder brother.

The royal brothers are expected to meet in a few weeks at the unveiling of their mother Princess Diana's statue at Kensington Palace, though Harry's attendance is in doubt as his daughter will be less than a month old at the time. The event is being held on July 1, on what would have been the late Princess's 60th birthday.

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Meghan Markle and Catherine, Duchess of Cambridge Chris Jackson/Getty