The Duchess of Sussex, 43, wrote on Instagram: “The best. Happy Father’s Day to our favourite guy.”
The United States and Britain celebrated Father’s Day on Sunday.
The more close-up images in the post suggest a departure from the duchess’ usual rule of only showing the children from the back in order to preserve their privacy.
In the latest post, the children’s faces are shown in full in older photographs and videos of them as infants.
Only the backs of the prince and princess’ heads feature in the more recent footage.
The duchess has been active on Instagram in recent weeks, sharing more private family moments than before.
Marking Lilibet’s 4th birthday on June 4, she posted a series of photographs of intimate moments from her daughter’s life as well as video of her with the duke and their children at Disneyland.
One post included black and white portraits of Meghan holding the infant princess, as well as a more recent image of the pair hugging on a beach.
A throwback video posted on the princess’ birthday showed the duchess twerking while pregnant as Prince Harry danced around her in a hospital room.
Another post featured tender moments between Prince Harry and “Daddy’s little girl and favourite adventurer”.
“The sweetest bond to watch unfold,” the duchess wrote below photographs that included one of Harry cradling his newborn daughter.