Harry, 42, the King's younger son, caused a huge rupture in the royal family when he and his wife Meghan quit royal duties and moved to California in 2020 from where they were highly critical of the institution.
He has barely spoken to his older brother, heir Prince William, for years, and his family has only recently met up again with his father.
In an interview with GQ magazine, Harry, who relocated back to the United Kingdom in August with Meghan and their two children, said he wanted to patch things up.
"With everything else that's going on in the world, the most important thing is to reconcile," he told GQ.
He said he could understand the fascination with his family's situation as people could relate to it.
"There's sibling disagreements, there's broken relationships between kids and their parents, kids and one parent," he said.
Some people might be inspired by efforts to reconcile and this could help their own relationships.
"And some people don't want it to work out. I want it to work out," he added.
Harry's spokesperson said those latter comments were not meant as a swipe at William or any other family members.
Harry, the Duke of Sussex, went on to tell GQ that while "scars stick around forever," he wanted to encourage everybody to let go of the past.
"For me, there's enough drama in the world and enough drama in people's lives than to continue with issues with family," he said.
"It's not worth it."
In the lengthy interview, Harry also discussed themes he has previously talked about, such as the effect of losing his mother Princess Diana when he was 12 and his mental health struggles.
But he also talked about why he had returned to the UK, saying that being able to put his children in a British school "has meant a lot to me".
"I didn't know how important it was to me. I always thought it was going to be something that we would try and do, but now they've been in school for two weeks. They're loving it and it's just giving them a whole different experience."
He also said he hoped that his fraught relationship with the UK press, which partly led to him leaving in the first place and has led to a number of lawsuits against newspaper groups, would now be better.
"My hope is that it will change," he said.
"There have been some battles that have been fought, necessarily so. But hopefully we can all draw a line under that.
"As with everything else that's going on in the world, there's aspects of the past that I'm sure all of us, me, my family, some of the British press, that we'd all like to leave behind us and work for the greater good."
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