The Mail on Sunday says it will "vigorously" defend itself in a court case launched by the couple.
It was announced on Tuesday that the Duchess of Sussex is suing the paper over a claim it unlawfully published a private letter Meghan sent to her father, Thomas Markle, earlier this year.
Prince Harry revealed the news in a lengthy statement, stating that the legal action was in response to "relentless propaganda".
According to the BBC, a Mail on Sunday spokesman said the paper stood by the story it published.
The paper is accused of an "intrusive and unlawful publication of a private letter" and of a campaign of publishing false and derogatory stories about the Duchess of Sussex.
Prince Harry said "positive" coverage of the couple's tour of Africa had exposed the "double standards" of "this specific press pack that has vilified [Meghan] almost daily for the past nine months".
Referring to his late mother Diana, Princess of Wales, Prince Harry said his "deepest fear is history repeating itself".
Prince Harry said: "I lost my mother, and now I watch my wife falling victim to the same powerful forces."
The royal couple – with son Archie in tow – spent the last day of their African tour visiting Tembisa township, near Johannesburg, to learn about a scheme to tackle youth unemployment.
They also met with Nelson Mendela's widow, Graca Machel.