"Meghan loved seeing all the other royal children and was doting on them," the source added.
After welcoming her first child, Markle made her first public appearance at the ceremony, on Saturday. The source also revealed that the Duchess has "always been great with kids, but seemed to gravitate to them more" during the parade.
Markle made her debut at the ceremony held in honour of the Queen's 93rd birthday. She wore a navy ensemble, designed by her wedding dress designer Clare Waight Keller and paired it with a matching hat by Noel Stewart.
Duke and Duchess of Sussex, Prince Harry and Meghan Markle, rode in a carriage together with Duchess of Cambridge, Kate Middleton, and Camilla, Duchess of Cornwall.
Prince Harry and Markle welcomed their baby boy, Archie Harrison Mountbatten-Windsor, on May 6 ahead of their first wedding anniversary.