"Having played a tank troop we want to show our support for the Invictus Games and our wounded warriors," said Brad in the short 30-second clip.
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"It's going to be really inspirational event and so we hope everyone will join us in getting behind the Invictus Games," added young actor Logan.
The games are a Paralympic-style sporting competition for wounded servicemen and women that the royal launched earlier this year. The British team is made up of veterans and current members of the armed forces who will compete against 14 other nations. Some 69 per cent come from the army, 23 per cent from the naval service and eight per cent from the royal air force.
Harry – who is known as Captain Henry Wales in his military role – decided to launch the Invictus Games after "stealing" the idea of the Warrior Games in America. Invictus is the Latin for unconquered – a word that embodies the fighting spirit of the wounded and injured and what they can achieve post-injury.
Set in the final months of WWII, Fury follows Brad's battle-weary sergeant Wardaddy and his tank which often goes behind enemy lines for the Allies.
Prince Harry promoting the Invictus Games
Filmed entirely in the British countryside, the film also stars The Avengers' Mark Ruffalo, and Shia LaBeouf, and in order to maintain authenticity, a British D-Day veteran was personally invited to the set by Brad.
Peter Comfort, 90, met the Hollywood superstar but admitted he had to use Google beforehand to find out who Brad was.
"Mr Pitt was very friendly and charming actually but I didn't know who he was," the WWII veteran said.
Fury will premiere in the UK as the closing night gala at this year's London Film Festival.
You can buy tickets for the Invictus Games here - http://invictusgames.org/ticket-info/