The Queen has agreed a "period of transition" in which the Duke and Duchess of Sussex will spend time in Canada and the UK.
Photo: Tolga Akmen / AFP
She said she is "entirely supportive" of their desire for a new role but "would have preferred" them to remain full-time working royals.
She expects final decisions to be made in the coming days, she said.
Senior royals have been in talks about Prince Harry and Meghan's role after they said they wanted to "step back".
In a statement, the Queen said the talks at Sandringham, which also involved the Prince of Wales and the Duke of Cambridge, had been "very constructive".
"My family and I are entirely supportive of Harry and Meghan's desire to create a new life as a young family," she said.
'More independent life'
"Although we would have preferred them to remain full-time working members of the Royal Family, we respect and understand their wish to live a more independent life as a family while remaining a valued part of my family."
She said that it has been agreed that there will be "a period of transition in which the Sussexes will spend time in Canada and the UK" after Harry and Meghan "made clear that they do not want to be reliant on public funds in their new lives".
"These are complex matters for my family to resolve, and there is some more work to be done, but I have asked for final decisions to be reached in the coming days," she said.
The urgent talks were convened after the Sussexes surprised the rest of the Royal Family on Wednesday with a statement expressing their desire for a "new progressive role", where they would be financially independent and divide their time between the UK and North America.
The talks took place as Prince Harry and Prince William issued a joint statement denying "false claims" that their relationship had been damaged by "bullying" on the part of the older brother.
They said that the "inflammatory language" was "offensive" and "potentially harmful", given their support for mental health causes.
Historian Robert Lacey told the BBC Radio 4's PM programme the Queen's statement following the meeting was unusually personal, with several references to "my family" and "my grandson".
"It is remarkably hands-on. I mean it may have been processed through officials but this is the Queen, speaking to her people and speaking about her family, and I think coming right through it is the concern she feels," he said.
Instead of using the formal titles of the couple - the Duke and Duchess of Sussex - the Queen simply called them "Harry and Meghan".
How did we get here?
In their statement on Thursday NZ time, posted on the couple's official Instagram account, the duke and duchess said they intend to "step back" as senior royals, spending time in North America, while "continuing to honour our duty to the Queen, the Commonwealth, and our patronages".
It came after an interview last October, when Prince Harry and Meghan publicly revealed their struggles under the media spotlight.
The couple were already preparing to launch their own Sussex Royal charity, which they set up after splitting from the Duke and Duchess of Cambridge's foundation in June last year.
It was revealed in December that the couple had made an application to trademark their Sussex Royal brand for items including books, calendars, clothing, charitable fundraising, education and social care services.
- BBC