Watch: Paul Burrell: Prince Harry will be 'torn' when he returns to the US
Prince Harry's trip to the UK "broke the ice" for future conversations with his family but "outstanding issues have not been addressed", according to a source.
Harry was in the UK for the funeral of his grandfather the Duke of Edinburgh, which took place on 17 April in Windsor Castle.
Omid Scobie, biographer of Harry and his wife Meghan Markle, confirmed the Duke of Sussex arrived back in the US on Tuesday, the day before his grandmother's 95th birthday.
Scobie reported a source close to Harry said: "This trip was to honour the life of his grandfather and support his grandmother and relatives.
"It was very much a family-focused period of time. Saturday broke the ice for future conversations but outstanding issues have not been addressed at any great length. The family simply put their issues to one side to focus on what mattered."
Harry, 36, was separated from his brother Prince William in the procession behind Prince Philip's funeral, with their cousin Peter Phillips in between them.
But the two brothers were seen chatting as they left St George's Chapel, where the service was held, after William's wife Kate made the first approach to Harry.
There have long been reports of a rift between Harry and William, which were not helped by an interview Harry did with Oprah Winfrey in March.
Watch: Prince Philip's funeral: William and Harry leave chapel together after ceremony
He and his wife said there had been a racist remark made about their son Archie before he was born, leaving William to defend his family as "very much not racist".
And Meghan said the palace had failed to correct a story in newspapers that claimed she had made the Duchess of Cambridge cry before their 2018 wedding.
Meghan said it was Kate who made her cry before she married Harry, and that Kate had apologised and sent flowers.
Scobie said reports that Harry wrote a letter to his father Prince Charles were incorrect.
Charles is understood to be staying in Llwynywermod, near Llandovery, his rural Welsh home.
Harry had to go into quarantine when he arrived in the UK because there are currently no travel corridors in place.
However he would have been granted time out of quarantine for the funeral as there are exemptions on compassionate grounds.
It also appears Harry took the option of a private COVID test to get out of quarantine early, as Harper's Bazaar reported he was out after five days.
UK government guidelines currently indicate a test must be taken by day two and day eight of the 10-day isolation period, but visitors can opt to pay for a test from an approved private supplier at five days instead, meaning they can leave earlier.
Harry stayed at Frogmore Cottage, the Windsor home the Queen gave him and Meghan when they got married.
It's understood his cousin Princess Eugenie and her husband Jack Brooksbank are currently living there with their son August, so Harry may have been able to spend time with them if he cleared quarantine early.
Harry had to travel alone to the funeral because Meghan could not get medical permission to fly. She is expecting their second child, a daughter, and has said she is due in the summer.
Watch: The wonderful life of Prince Philip, The Duke of Edinburgh