Sir John, who was guardian to Princes William and Harry following their mother's death, said he hoped it would end any "friction" between the pair.

He also said the Queen needed time to grieve for her husband.

His comments came as the Archbishop of Canterbury paid tribute to the duke in a remembrance service.

The Queen has described the death of her husband as "having left a huge void in her life", the Duke of York has said.

During a service at Canterbury Cathedral earlier, which was also streamed online, Archbishop of Canterbury Justin Welby said that "for the Royal Family, as for every other, no words can reach into the depth of sorrow that goes into bereavement".

The archbishop is also expected to lead the duke's funeral on Saturday, which Princes William and Harry are both due to attend.

The Duke of Sussex will fly from the US for the service, though it is not clear when.

His wife, Meghan Markle, who is pregnant, will remain at home in California on the advice of doctors.

Members of the Royal Family will walk behind the coffin ahead of the funeral at Windsor Castle.

Cardinal Vincent Nichols, the head of the Catholic Church in England and Wales, has suggested that coming together for Philip's funeral could help to heal any tensions.

Sir John, who was appointed a special guardian to the princes after their mother, Diana, Princess of Wales, died in 1997, told BBC One's Andrew Marr Show: "The friction that we are told has arisen is a friction better ended as speedily as possible."

He added: "They shared emotion. They share grief at the present time because of the death of their grandfather. I think [this] is an ideal opportunity.

"I hope very much that it is possible to mend any rifts that may exist."

Harry and Meghan, who have stepped back from frontline royal duties, gave an interview to US broadcaster Oprah Winfrey last month.

In it, Harry said of his older brother: "The relationship is 'space' at the moment. And time heals all things, hopefully."

Sir John also told Andrew Marr the Duke of Edinburgh would "still be there in [the Queen's] memory" and that she would "hear his voice".

Being head of state was a "lonely position in many ways" for the Queen, and the duke was "the person to whom she could unburden herself", he added.

A period of national mourning will end after 17 April, when Prince Philip's funeral takes place at Windsor Castle's St George's Chapel.

A national minute's silence will be held to coincide with the start of the service at 15:00 BST.

Prince Philip died at Windsor Castle on Friday, aged 99.

In an interview at a service in Windsor, Prince Andrew said he loved his father, who was "always somebody you could go to" - and that his death was a "terrible loss".

He added: "We've lost the grandfather of the nation."

Members of the public have continued laying flowers outside the castle, although the new government guidance asks the public to refrain from doing so and give to charity instead.

A spokesman for Windsor Great Park said on Saturday that tributes would be removed "respectfully" and displayed within the castle grounds.

Royal household staff were photographed on Sunday placing bouquets on the ground outside St George's Chapel.

Joanna Lumley was among those to pay their respects to Prince Philip on BBC One's Andrew Marr Show.