Prince Andrew said his father's death was a "terrible loss", and his family was "rallying round" to help the Queen.
"We've lost the grandfather of the nation," he added, as he left a service at Windsor.
Earlier, ex-PM Sir John Major said the Royal Family's shared grief was an "ideal opportunity" to mend any rifts.
And during a special service at Canterbury Cathedral, the Archbishop of Canterbury Justin Welby paid tribute to Prince Philip, saying that "for the Royal Family, as for every other, no words can reach into the depth of sorrow that goes into bereavement".
The archbishop, who is expected to lead the duke's funeral service at Windsor Castle on Saturday, said Prince Philip showed "a remarkable willingness to take the hand he was dealt in life and straightforwardly to follow its call, to search its meaning, to go out and on as sent to inquire and think, to trust and to pray".
Prince Andrew was joined by the Earl and Countess of Wessex and their daughter Lady Louise Windsor at a separate service at Windsor's Royal Lodge.
He said the Royal Family was grateful for all the "absolutely amazing tributes" to Prince Philip.
He added: "The Queen, as you would expect, is an incredibly stoic person.
"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."
Speaking of his love for his father, Prince Andrew said: "He was so calm. If you had a problem, he would think about it.
"He was always somebody you could go to and he would always listen so it's a great loss.
"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."
He added: "I know there is a huge amount of support, not just for her (the Queen) but for everybody as we go through this enormous change."
Prince Andrew stepped back from royal duties in 2019 after criticism of his ties to convicted sex offender Jeffrey Epstein intensified following a BBC interview.
The Earl of Wessex, the Queen's youngest son, said: "However much one tries to prepare oneself for something like this, it's still a dreadful shock.
"And we're still trying to come to terms with that. And it's very, very sad.
"But I have to say that the extraordinary tribute and the memories that everybody has had and been willing to share has been so fantastic."