The Duke of Sussex made his first appearance since returning to the UK on Monday.
He began by saying: "I'd like to start by acknowledging and celebrating the incredible young people joining us today. And wherever you are right now, I want to thank you for being part of this important moment and for being such a valuable asset to your community.
"I'm truly honoured to be celebrating your work, your commitment to change making and the vital role that you've taken on representing a new generation of humanitarianism."
WATCH: Prince Harry makes surprise appearance at the 2021 Diana Awards
The Duke landed in the UK last Friday ahead of the unveiling of a statue of Diana, Princess of Wales at Kensington Palace on Thursday.
Harry will be reunited with his brother, Prince William, at the unveiling on 1 July – which would have marked their mother's 60th birthday.
He continued: "Later this week, my brother and I are recognising what would have been our mum's 60th birthday, and she would be so proud of you all for living authentic life with purpose and with compassion for others.
"Our mum believed that young people have the power to change the world. She believed in your strength because she saw it day in and day out and in the faces of young people exactly like you, she witnessed a boundless enthusiasm and passion.
"And I too see those same values shine through as it has done for 21 years now, The Diana Award carries her legacy forward by putting young people at the centre of our future. And this has never been more important."
Prince Harry appeared in a video message at the virtual Diana Awards
Harry's wife, Meghan, and their two children, Archie, two, and Lilibet, who was born on 4 June, have remained in the US.
Speaking of his wife, Harry said: "And Meg and I fundamentally believe that our world is at the cusp of change, real change for the good of all. But the question before us is what that change will look like.
"The Covid-19 crisis exposed severe inequities and imbalances around the world. We saw the disproportionate effect of this pandemic on communities of colour, on women, on underserved communities and on less wealthy countries.
"We've seen and unless we take swift action, we will continue to see a disparity in our humanitarian and moral obligation to vaccinate the world.
"There is great need for young leadership and there is no greater time to be a young leader. I believe in you. We believe in you. And that belief in your own ability to change the world in doing the right thing is what makes you a force to be reckoned with."
William and Harry at the Diana Award's Legacy Awards in 2017
Harry finished his message by saying: "To all the 2021 Diana Award recipients thank you for inspiring us with your brilliance, your determination and your compassion, your actions hold the potential to leave a life changing impact. You are putting the 'do's' behind the 'say's', and this is the personification of our mother's legacy.
"To everyone else watching. I'm hopeful that today's Award recipients have inspired you to be part of a future where humanity is cherished, where our communities are supported and uplifted, and where we are considerate and compassionate to each other, both online and off.
"Never be afraid to do what's right. Stand up for what you believe in and trust that when you live by truth and in service to others, people will see that just as they did with my mum."
Throughout his visit to the UK, the Duke of Sussex is staying at the Sussexes' Windsor residence, Frogmore Cottage, where his cousin, Princess Eugenie, now lives with her husband Jack Brooksbank and their baby son August, who was born in February.
He must self-isolate for five days until he is able to do a 'test to release', which will allow him to leave self-isolation once he receives a negative result.
Last year, Harry called in from Los Angeles to make a surprise appearance at the first virtual Diana Award ceremony.
The Diana Award was established in 1999 in memory of Diana, Princess of Wales, and her belief that young people have the power to change the world.
The charity, which runs anti-bullying and mentoring programmes, also rewards young people who carry out inspiring work. Each year thousands of young people are nominated by individuals and their communities to highlight these selfless acts.
For more information about the Diana Award, visit diana.award.org.uk.
Make sure you never miss a ROYAL story! Sign up to our newsletter to get all of our celebrity, royal and lifestyle news delivered directly to your inbox.