Buckingham Palace said the Queen called for an end to the marriage in a letter to each of them earlier this week.
It is understood the prince has replied in agreement with his mother but the princess has yet to respond, according to a Palace spokesman.
"After considering the present situation the Queen wrote to both the prince and princess earlier this week and gave them her view, supported by the Duke of Edinburgh, that an early divorce is desirable," the spokesman said.
"The Prince of Wales also takes this view and has made this known to the Princess of Wales since the letter.
"The Queen and the Duke of Edinburgh will continue to do all they can to help and support the Prince and Princess of Wales, and most particularly their children, in this difficult period."
The Queen's action comes just weeks after the princess's interview on Panorama which sparked a national debate on the future of the monarchy.
In it she said she did not want a divorce and claimed there were "three people" in their marriage because of Charles' friendship with Camilla Parker Bowles.
Diana was also repeatedly critical of her husband's ability to become king, his family, and their advisers and also admitted committing adultery herself.
Constitutional experts have said divorce would mean the Princess of Wales could never become queen.
The prime minister and senior Privy Councillors have backed the Queen's decision after prolonged private talks over the last two weeks.
Buckingham Palace's announcement followed discussions between the Queen and the Prime Minister.
Mr Major, who announced the couple's original separation in the Commons in 1992, will make a further statement to MPs once divorce proceedings are under way.E-mail this story to a friend
The couple married in 1981
In Context The "fairytale" marriage of the Prince and Princess of Wales ended with a "decree nisi" on 28 August 1996.
It was a far cry from their lavish wedding at St Paul's Cathedral 15 years earlier, witnessed by a television audience of millions.
As part of the divorce settlement Diana was stripped of her royal title - HRH - and instead became known as Diana, Princess of Wales.
It is understood she was awarded a �17m lump sum and �350,000 a year to run her private office, while Diana and Charles agreed to share custody of their sons.
Almost exactly a year later Diana died in a car crash with her companion Dodi Fayed in Paris.
Prince Charles married Camilla Parker Bowles in April 2005.
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