Harry, 34, travelled to The Hague in the Netherlands to officially launch the one year countdown to the Invictus Games, taking place there in 2020.
The prince joined a training session at the Sportcampus Zuiderpark where he watched wheelchair basketball and archery demonstrations.
At one point the new father tried his hand at archery, hitting the bullseye on his first attempt.
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BULLSEYE! Hard to see from here but Harry just hit the target on his first attempt at the archery! ARCHIE-ERY. I’ll get my coat. @InvictusGamesNL @ukinnl @WeAreInvictus #archie pic.twitter.com/gSwvCs8DMb— Emily Nash (@emynash) May 9, 2019
Harry will return home to Frogmore Cottage in Windsor later today.
His trip to the Netherlands was originally meant to be a two-day visit, but palace aides at the time said that his plans may be changed, depending on whether Meghan had gone into labour or not.
The duke was also given some presents for his newborn son, including a soft toy rattle and an Invictus Games babygrow presented by Princess Margriet of the Netherlands.
Later in the day, Harry donned an Invictus Games jacket embroidered with the word ‘Daddy’ underneath the logo, as he cycled around Zuiderpark.
The Invictus Games use the power of sport to inspire recovery, support rehabilitation and generate a wider understanding and respect for wounded, injured and sick Servicemen and women.
Harry launched the Games in London in 2014 and subsequent events have been held in Orlando (2016), Toronto (2017) and Sydney (2018).
During a speech, the duke spoke about the importance of mental health.
He said: “Our mental fitness is the key, because without it we fail to operate efficiently; but with it your physical performance and potential are exponentially improved and we have witnessed this over and over again.”
On Wednesday, the Duke and Duchess of Sussex introduced their baby boy, named Archie Harrison Mountbatten-Windsor during a brief photo opportunity in St George’s Hall at Windsor Castle.
During the interview new mum Meghan, 37, described parenthood as “magic,” adding that she is “really happy” to “have the two best guys in the world”.
Harry, who was holding his son in his arms throughout, said: "It's great. Parenting is amazing. It's only been two and a half days, three days, but we're just so thrilled to have our own little bundle of joy and be able to spend some precious times with him as he slowly, slowly starts to grow up."
The royal tot was born at 05:26, weighing 7lb 3oz, on May 6, 2019. The location of Archie’s birth has not been confirmed by the palace, but reports have emerged that Meghan was taken to a London hospital on Sunday night.
The couple have decided not to give their newborn a title (they could have used one of Harry’s subsidiaries Earl of Dumbarton) and instead he will be known as Archie Harrison Mountbatten-Windsor.
When Harry’s father Prince Charles becomes king, Archie would then be eligible to become a prince, as he will be a grandson of the Sovereign.