The Queen and the rest of the royal family have asked that well-wishers not to gather in crowds to pay their respects to Prince Philip.
In a second statement from Buckingham Palace, they asked members of the public consider making a donation to a charity instead of leaving floral tributes.
They also announced that an online Book of Condolence has now been set up on the royal family's website.
The Queen also confirmed that she is modifying funeral arrangements in light of the Covid pandemic, saying details will be released in coming days.
The royal family's website has now been completely update to pay respects to Prince Philip, who died this morning.
There is information about his life, charity work and his dedication to the royal family.
The statement read: "During the coronavirus pandemic, and in light of current Government advice and social distancing guidelines, modified Funeral and ceremonial arrangements for His Royal Highness The Duke of Edinburgh are being considered by Her Majesty The Queen. Details will be confirmed in due course.
"In accordance with public health advice, members of the public are asked to continue to follow the current Government guidance, not to gather in crowds, and not to visit Royal residences to pay their respects.
"During this time the Royal Family ask that members of the public consider making a donation to a charity instead of leaving floral tributes in memory of The Duke of Edinburgh.
"An online Book of Condolence for those who wish to leave messages is available on this website.
"Union flags have been half-masted at all Royal residences flying the Union flag. The Royal Standard will continue to fly at Windsor Castle where The Queen is in residence."
Prince Philip passed away this morning at Windsor Castle.
It followed his longest every hospital stay earlier this year.
