After attending a church service on Sunday where members of the Royal Family said prayers for Prince Philip as the nation remembered him, Prince Andrew said the death of his father was resonating with many people.
"We've lost almost the grandfather of the nation," he said.
His brother, Prince Edward the Earl of Wessex, said Philip's death was a "dreadful shock" and the family was still "trying to come to terms with that".
The Countess of Wessex candidly described the circumstances of his death as "very peaceful", saying it was as if "somebody took him by the hand and off he went".
Later, the Princess Royal paid her own tribute, describing her father as "my teacher, my supporter and my critic".
Andrew said the Royal Family were now rallying around the Queen in her grief as she comes to terms with the loss of her partner of more than 70 years.
"The Queen, as you would expect, is an incredibly stoic person," he said.
"She described it as having left a huge void in her life but we, the family, the ones that are close, are rallying round to make sure that we're there to support her."
Sophie and Edward appeared visibly moved as they spoke about the Queen, with their daughter by their side, after the service.
The Queen is "thinking of others before herself", the countess said, and Edward added: "As always. But bearing up, and again it's just that wave of affection for him and just those lovely stories.
"They just mean so much and the tributes have been just fantastic. That's really, really important and we really do appreciate it."
Speaking separately after the service, Andrew said the family was grateful for all the "absolutely amazing tributes" to his father.
"He was a remarkable man," he said.
"I loved him as a father. He was so calm. If you had a problem, he would think about it.
"That's the great thing that I always think about, that he was always somebody you could go to and he would always listen so it's a great loss," he added.
"We've lost almost the grandfather of the nation. And I feel very sorry and supportive of my mother who's feeling it probably more than everybody else."
The monarchy is observing two weeks of royal mourning and the members of the family who attended church in Windsor were dressed in black, with Andrew and Edward also wearing black ties.
The Duke of Edinburgh's funeral will be held on Saturday at Windsor Castle.
Only 30 people – expected to be his children, grandchildren and other close family – will attend as guests, but the Duchess of Sussex has been advised by her doctor not to travel to the UK for the funeral, a palace spokesman said.
All public elements of the funeral – to take place entirely in the grounds of the castle – have been cancelled, but it will be televised.
Cover image: The Queen with the Duke of Edinburgh ahead of his 99th birthday (Picture: PA).