Prince Harry and Meghan posted a picture of baby Archie's feet on their official Instagram account, writing: "Paying tribute to all mothers today - past, present, mothers-to-be, and those lost but forever remembered.

"We honour and celebrate each and every one of you."

The "lost but forever remembered" was widely interpreted to be a reference to Harry's mother, Diana, who died in a Paris car accident in 1997.

The photo was taken against a backdrop of forget-me-nots - believed to have been one of Princess Diana's favourite flowers.

It was Meghan's first Mother's Day. She gave birth in the early hours of Monday morning to Archie Harrison Mountbatten-Windsor, leaving his father, Queen Elizabeth's grandson, and royal fans across the world enthralled. He is seventh in line to the British throne.

The American spelling of "honor" suggests the duchess wrote the post.

Britain celebrates Mother's Day on March 22, but the US, Australia, Canada, New Zealand, South Africa, Kenya, Japan and several other countries mark it on the second Sunday in May.

The couple also quoted from the poem Lands by US poet Nayyirah Waheed: "My mother was my first country; The first place I ever lived."

Archie is set to meet his uncle and aunt, the Duke and Duchess of Cambridge, at Windsor on Monday. The Prince of Wales and the Duchess of Cornwall, are also expected to visit this week following recent official engagements in Germany.

He has already met the Queen and Duke of Edinburgh, while his grandmother, Meghan's mother Doria Ragland, has been on hand since the birth.

Other visitors have included Lady Jane Fellowes, Diana's sister.

- AAP/Reuters