The Mail on Sunday said: "An article on 25 October 2020 reported that Prince Harry had been accused by a top general of turning his back on the Royal Marines since withdrawing from his military roles in March and that, in an apparent snub to the Armed Forces, he had failed to reply to a letter from Lord Dannatt, a former Chief of the General Staff.
"We now understand that Harry has been in contact in a private capacity with individuals in the military including in the Royal Marines to offer informal support since March and that whilst he did not initially receive the letter from Lord Dannatt referred to in the article due to administrative issues he has since replied on becoming aware of it. We apologise to Prince Harry and have made a donation to the Invictus Games Foundation."
The Duchess of Sussex is also suing Associated for breach of privacy and copyright after The Mail on Sunday published extracts of a letter she sent to Thomas Markle, her father.
The trial had been scheduled for January but the Duchess successfully applied for an adjournment on confidential grounds and it will now be heard next autumn.
However, an application for a summary judgment, which would see the case resolved by the judge without a full trial, will be heard next month.
The Duke is also suing The Sun and Daily Mirror for alleged phone hacking, claiming his voicemails had been illegally intercepted.
In July, it emerged that the couple were suing paparazzi for invasion of privacy after drones were allegedly used to take pictures of their son, Archie, at the house where they were staying in Los Angeles.
The Duchess has settled a claim against Splash News, the picture agency, over claims her privacy was breached when she was "papped" on a walk with Archie, then eight months, and her dogs on Vancouver Island, Canada, in January.
Splash has agreed not to take any photos of the family should it come out of administration, the High Court heard earlier this month.
The Duke and Duchess are hoping to spend more time in the UK next year, but plans to attend events to mark the Duke of Edinburgh's 100th birthday celebrations and the unveiling of a statue of Diana, Princess of Wales, on July 1, which would have been her 60th birthday, are dependent on coronavirus restrictions.
A source close to the couple dismissed claims that the couple were planning to return to the UK in the New Year to broker an extension to deal with Buckingham Palace over their new working lives away from the Royal Family. A 12-month review period expires on March 31.