In his capacity as founder of the Invictus Games Foundation, which helps soldiers through their recovery via international sports competitions, Harry said the situation in Afghanistan "resonates" with past participants.
The duke spent 10 years in the Army, which included two frontline tours to Afghanistan.
As harrowing videos of civilians' desperate attempts to flee from Kabul airport were broadcast around the world after the Taliban captured the capital, the duke issued a joint statement with senior figures from the Games.
The statement read: "What's happening in Afghanistan resonates across the international Invictus community.
"Many of the participating nations and competitors in the Invictus Games family are bound by a shared experience of serving in Afghanistan over the past two decades, and for several years, we have competed alongside Invictus Games Team Afghanistan.
"We encourage everybody across the Invictus network - and the wider military community - to reach out to each other and offer support for one another."
The Invictus Games has been postponed for two years running due to the coronavirus pandemic, and the next competition is due to be held in The Hague, Holland, in 2022.
Organisers considered staging the event for sick, wounded and injured veterans and serving military later in the year, and even digitally, but wanted to preserve the experience for competitors and provide them with certainty.
Harry was inspired to found the global tournament after attending the Warrior Games in Colorado in 2013 and seeing how injured American military personnel thrived on the challenge of taking part in competitive sports that aided their recovery.