Prince Harry and Meghan Markle have celebrated Father’s Day in the UK by sharing a new image of their six-week-old son Archie.

The sepia-toned photo of the royal baby staring at the camera and gripping his dad’s left hand was shared on the SussexRoyal Instagram account on Monday morning (Australian time).

Prince Harry’s wedding ring is also visible in the picture.

“Happy Father’s Day! And wishing a very special first Father’s Day to The Duke of Sussex,” the caption read.

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A post shared by The Duke and Duchess of Sussex (@sussexroyal)

Prince Charles and Prince William also shared Father’s Day posts on Sunday.

In a message on the Clarence House Twitter page, Charles shared good wishes with “Dads everywhere” alongside an image of him with his two sons.

To Dads everywhere, have a wonderful #FathersDay.
📸 Chris Jackson / Getty pic.twitter.com/ydQFdhxG6A

— Clarence House (@ClarenceHouse) June 16, 2019

The UK and the US both celebrate Father’s Day on the third Sunday in June. Australia traditionally observes the day on the first Sunday of September.

William marked the occasion by sharing two photos – one of him walking beside Charles and a more recent picture of Prince Louis playing on a rope swing in the Duchess of Cambridge’s Chelsea Flower Show garden.

William and Kate’s two other children, Prince George, 5 and Princess Charlotte, 4, were not part of the tribute. Also missing from the couple’s post was any mention of Kate’s own father, Michael Middleton.

The absences were noted by the couple’s social media followers, with one posting: “Sorry, I don’t agree with the photo’s choice. Where are Charlotte and George? Where is Kate’s father?”

A second added: “Apparently Kate doesn’t have a dad and William only has one child. Happy fathers day!”

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A post shared by The Prince and Princess of Wales (@princeandprincessofwales)

Harry and his Meghan have been enjoying life as a family of three after welcoming their firstborn on May 6.

The Duke and Duchess of Sussex are raising Archie Mountbatten-Windsor, the seventh in line to the British throne, in the sanctuary of Frogmore Cottage – their new home in Windsor Home Park, Berkshire, close to the Queen’s residence at Windsor Castle.

Meghan left Archie for a couple of hours earlier this month to join the royal family for the annual Trooping the Colour celebration in honour of the Queen’s birthday.

The Duchess of Sussex broke her maternity leave to sit next to Harry in a horse-drawn carriage for the ride down The Mall to Buckingham Palace.

-with AAP