London — After an unprecedented meeting at her home in eastern England, Britain's Queen Elizabeth II said in a statement Monday that the royal family was "supportive" of Meghan and Harry's decision to split their time between the United Kingdom and Canada, though they would have "preferred" a different arrangement.

"Today my family had very constructive discussions on the future of my grandson and his family," the queen said in the statement put out by Buckingham Palace.

"My family and I are entirely supportive of Harry and Meghan's desire to create a new life as a young family. 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 continued.

The queen, Harry, his brother William and his father Prince Charles had been meeting at the queen's estate in Sandringham, England in a family summit called after Harry and Meghan said they wanted to pull out of their "senior" royal duties and spend more time in North America. CBS News was told that Meghan might have taken part in the meeting by phone.

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"Harry and Meghan have made clear that they do not want to be reliant on public funds in their new lives," the queen's statement said.

"It has therefore been agreed that there will be a period of transition in which the Sussexes will spend time in Canada and the UK.

"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 concluded.

In Monday's meeting, the monarch and the senior members of her family were expected to try and hash out Harry and Meghan's role going forward, including who's to pay for their transatlantic lifestyle. Details include the kind of security they'll need — something that, until now has been paid for by British taxpayers, how they'll be able to keep their home near Windsor Castle, Frogmore Cottage, and what commercial deals they'll be allowed to strike.

The crisis has sparked frenzied speculation in the media, from a backlash aimed at Meghan, to claims that she and Harry felt "bullied" by Prince William.

The brothers firmly denied that claim in a statement issued Monday morning, but there has been tension between them, felt by Prince William, according to royal reporter Roya Nikkhah.

"I think he (Prince William) feels very sad that there's been this split that's seen them go into what he describes as separate entities. He talked about not being able to put his arm around his brother anymore and that makes him sad," Nikkhah said.