Prince Harry told Oprah Winfrey that the UK tabloid media is "bigoted" and creates a "toxic environment" of "control and fear".
He said he thought the Prince of Wales had to "make peace with it".
The Society of Editors said the media is not bigoted and is holding the "rich and powerful to account".
Meghan said social media had made the relationship with the press like "the wild, wild West" and said the Royal Family's press operation failed to defend her and Harry from untrue stories.
In the much-anticipated interview with Oprah, Harry and Meghan covered a range of deeply personal topics, including racism, mental health, their relationship with the media and Royal Family dynamics.
The two-hour interview was broadcast last night in the US and is due to be screened in the UK on ITV at 21:00 GMT on Monday night and on ITV Hub, courtesy of Harpo Productions/CBS.
In other key revelations:
* Meghan said she found life within the Royal Family so difficult that at times she "didn't want to be alive any more"
* She said Harry had been asked by an unnamed family member "how dark" their son Archie's skin might be
* Oprah later said the family member was not the Queen or the Duke of Edinburgh
* The couple announced their second child, which is due in the summer, is a girl
* They exchanged vows in a ceremony led by the Archbishop of Canterbury in their "backyard" three days before they were legally married at their public wedding in May 2018
* Harry said his brother and father were "trapped within the system" of the Royal Family
* He said his family cut him off financially at the beginning of last year and his father stopped taking his calls
* But Harry said he loved his brother "to bits" and wanted to heal his relationship with both him and his father
* Meghan said she phoned the Queen after Prince Philip went into hospital last month
US President Joe Biden's press secretary, Jen Psaki, said it had taken "courage" for Harry and Meghan to tell their own personal story and speak about struggles with mental health.
Asked about the claims that the Royal Family had failed to look after the Sussexes' mental health and that one family member had speculated on their unborn child's skin colour, Prime Minister Boris Johnson declined to comment, except to say he "always had the highest admiration for the Queen and the unifying role she plays".
He said "when it comes to matters to do with the Royal Family, the right thing for prime ministers to say is nothing", after being asked specifically if he believed the Royal Family was racist.
In previously unseen footage from the three hour 20 minutes interview, Oprah asked the prince if the couple left the UK because of racism. Prince Harry replied: "It was a large part of it."
He said that shortly after the couple announced they would step back from royal duties, someone who was "friends with a lot of the editors" had warned him about their confrontational stance with the press: "Please don't do this with the media, they will destroy your life."
The conversation happened at a fundraising dinner in January 2020, a few months after Meghan sued the Mail on Sunday over a private letter and Prince Harry said he feared his wife would fall "victim to the same powerful forces" that he lost his mother to.
The friend of the editors told him: "You need to understand that the UK is very bigoted." But the duke responded: "The UK is not bigoted, the UK press is bigoted, specifically the tabloids."
Speaking to Oprah, the prince added: "But, unfortunately, if the source of information is inherently corrupt or racist or biased then that filters out to the rest of society."
He said that "sadly" no-one in the family had said they were sorry that the couple felt they had to move away from royal life because they did not feel supported.
"The feeling is that this was our decision, therefore the consequences are on us."
He said it was "really hard because I am part of the system with them, I always have been".
Prince Harry said he is "very aware" that his brother Prince William "can't leave that system but I have".
Asked if William wanted to leave the system, he replied: "I don't know, I can't speak for him."
Harry said the "relationship and that control and the fear by the UK tabloids, it's a really, it's a toxic environment".
The duke said he will "always be there" for his brother and the rest of his family and he has "tried to help them to see what has happened".
His father, the Prince of Wales, "had to make peace" with the relationship with the media.
But Meghan said she and the duke could not make peace with it themselves, saying it was "different" because of social media, describing it as "like the wild, wild West".
The Society of Editors criticised the couple for accusing the media of racism without "any supporting evidence".
"The UK media has never shied away from holding a spotlight up to those in positions of power, celebrity or influence. If sometimes the questions asked are awkward and embarrassing, then so be it, but the press is most certainly not racist," said executive director Ian Murray.
In another unaired clip shared by broadcaster CBS on social media, Prince Harry said that in January last year the couple had an invitation to visit the Queen at Sandringham suddenly withdrawn by her private secretary, who said she was "busy all week".
"When you're head of the firm there are people around you that give you advice. And what has also made me really sad is some of that advice has been really bad," said Harry.
Also in the unaired footage, the Duchess of Sussex said her treatment in the press had been worse than other royals, saying that although the Duchess of Cambridge being branded "Waity Katie" before her marriage to Prince William must have been "really hard", it was "not the same".
"If a member of his family would comfortably say 'we've all had to deal with things that are rude', rude and racist are not the same," she said.
"And equally you've also had a press team that goes on the record to defend you, especially when they know something's not true, and that didn't happen for us."
Meghan said there had been an "obsession about anything in my world", including the media offering money to track down her parents.
"I did everything I could to protect both of them in that media frenzy for over a year," she told Oprah.
Success is walking from failure to failure with no loss of enthusiasm.