Philip, the husband of Britain's Queen Elizabeth who had been at her side throughout her record-breaking 69-year reign, died at Windsor Castle on Friday.
"As you can imagine, my family and I miss my father enormously," Charles, the couple's eldest son and heir to the throne, said outside his Highgrove House home in west England.
"My dear papa was a very special person who I think above all else would have been amazed by the reaction and the touching things that have been said about him and from that point of view we are, my family, deeply grateful for all that. It will sustain us in this particular loss and at this particularly sad time."
Buckingham Palace announced that the funeral for Philip would be held on April 17, and that the queen's grandson Prince Harry, who had become estranged from the family after moving to the United States with his wife Meghan, would attend.
Meghan, who is pregnant with their second child, will not attend on doctor's advice, the palace said.
The palace said long-established plans for the funeral had to be redrawn and scaled down because of Covid-19 restrictions, but they remained very much in line with Philip's wishes.
Philip, who was officially known as the Duke of Edinburgh, will be given a ceremonial royal funeral, not a state funeral, as planned before the pandemic. But there will be no public processions, and it will be held entirely within the grounds of Windsor Castle and limited to 30 mourners.
British Prime Minister Boris Johnson will not be among the guests in order to make space for as many family members as possible, his office said.
FUNERAL AT WINDSOR
"The occasion will still celebrate and recognise the Duke's life and his more than 70 years of service to the queen, the UK and the Commonwealth," a palace spokesman said.
The funeral, which will be broadcast on live television, will be held at the castle's St George's Chapel and will be preceded by a minute's silence across the country.
Charles and other members of the royal family will walk behind a specially-modified Land Rover, which Philip helped design. At the conclusion of the service, Philip will be interred in the Royal Vault.
Exact details of who will attending were not released, but among those present will be Harry, the Duke of Sussex, whose explosive interview with Oprah Winfrey alongside Meghan last month plunged the royal family into its greatest crisis in decades.
During the interview, Meghan said her pleas for help while she felt suicidal were ignored and that one unnamed member of the family had asked how dark their unborn child's skin might be. Harry also bemoaned his family’s reaction to their decision to step back from official duties and move to Los Angeles.
"The Duke of Sussex is planning to attend," the palace spokesman said. "The Duchess of Sussex has been advised by her physician not to travel. So the Duke will be attending."
Buckingham Palace stressed the service would be held in line with government coronavirus guidelines, meaning members of the royal family, including the queen, would be expected to wear a mask.
'QUEEN HAS BEEN AMAZING'
Tributes have flooded in from across Britain and from world leaders for Philip, who was a pillar of strength for the queen. At 94, she is the world's oldest and longest-reigning living monarch.
Philip was a decorated sailor who fought in World War Two and the armed forces marked his passing with artillery salutes with units in London, Edinburgh, Cardiff, Belfast and Gibraltar, and some navy warships, firing their guns.
The royal family asked the public to heed social distancing rules and avoid visits to its residences, but people still laid cards and bouquets outside Windsor Castle and Buckingham Palace.
"It's not something I've ever done before," said Joanna Reesby, 60, who came to pay her respects at Buckingham Palace. "I brought yellow roses for friendship because I think that's what he exhibited to everyone who came into his world."
The queen has lost her closest confidante. They had been married for 73 years and Philip would have turned 100 in June. Members of the family visited the grieving monarch at Windsor Castle.
"The queen has been amazing," said a tearful Sophie, the Countess of Wessex, as she left with her husband Prince Edward, the youngest son of Elizabeth and Philip.
On its official Twitter feed, the royal family put up a tribute paid by the queen to her husband on their 50th wedding anniversary in 1997.
"He has, quite simply, been my strength and stay all these years, and I, and his whole family, and this and many other countries, owe him a debt greater than he would ever claim, or we shall ever know," she said.
OFF-THE-CUFF REMARKS
While Philip's charm and disinclination to tolerate those he regarded as foolish or sycophantic earned him the respect of some Britons, many others found his sometimes brusque demeanour rude and aloof. He was fond of off-the-cuff remarks that were sometimes deemed racist and offensive.
Flags at Buckingham Palace and at government buildings across Britain have been lowered to half-mast and billboard operators replaced adverts with photographs and tributes to the prince. Sporting events observed silences in his honour.
A Greek prince, Philip married Elizabeth in 1947 and broke the news of her father's death five years later while they were visiting Kenya, meaning that she was queen at the age of 25.
He went on to play a key role helping the monarchy adapt to a changing world in the post-World War Two period, and also to support the queen as the monarchy faced numerous crises over the years. He finally stepped back from public duties in 2017.