Prince Charles meeting actor Leonardo DiCaprio at the royal premier on Thursday of The Man in the Iron Mask
He described the Princess, who spent time at Mr Blair's official country home, Chequers, with the Blair family and her two sons, as "a very remarkable individual" who could have contributed even more to the country had she lived.
Her death, he said, remains "a tragedy for everyone ... I felt at the time of her death, and I still feel now, a sense of personal loss".
Mr Blair made his remarks in a wide-ranging interview covering his thoughts on everything from President Clinton to Newcastle United. The interview was published in The Mirror newspaper on Friday.
He said his dislike of what had happened since Princess Diana's death was aimed not at memorabilia but at speculation about how she died.
He also insisted the Royal Family, particularly the Queen, were "very sensitive to how people felt" at the time of her death.
Asked, by the newspaper's editor Piers Morgan, if he thought the Prince of Wales would make a very good king, Mr Blair said: "Yes, certainly I do. And that's all I need say on the matter of Prince Charles."
Ministers defended
In the interview, Mr Blair fiercely defended some of his ministers who have faced controversy. However, he admitted it was legitimate for people to pass judgement on politicians' private lives.
He added: "I am not saying that problems in people's marriages never affect my judgement of people."
On the Lord Chancellor Lord Irvine, at the centre of controversy regarding the £650,000 refurbishment of his official residence, Mr Blair said: "You live and learn in politics - I'm sure that he will."
But he stressed the House of Lords money being spent on the work could not have been diverted to schools and hospitals.
He also praised Lord Irvine for putting together Labour's legislative programme "in record time.
"I don't, when a minister is being savaged in the media, simply throw him to the dogs and say 'that's it'," he added.
Mr Blair also said the Paymaster General, Geoffrey Robinson, had not avoided paying any UK tax. "He has paid more UK tax than certainly me," he said.
Support for the President
He also defended his support of the US President, Bill Clinton, who has been mired in claims of sexual impropriety.
He told the newspaper the President "has been a good President and a good friend to Britain.
"Those are perfectly good reasons for me to stand by him".
According to the newspaper, Mr Blair reportedly made clear he thought Newcastle United directors Freddy Shepherd and Douglas Hall, accused of insulting fans and players and calling local women "dogs", should be sacked.
The Prime Minister, a Newcastle fan, said: "I haven't thought of appointing either of them. All I would say that it's obviously a very sad and unfortunate incident."
He said that he could understand supporters' feelings, and that he was glad women in Newcastle "haven't lost their sense of humour", a reference to them barking from the stands in defiance at a recent match.
Mr Blair also said he had "a very high regard" for Formula 1 chief, Bernie Ecclestone, who he said had not expected anything in return for a donation to the Labour Party. The donation caused controversy and was later returned.
The 'Thatcher legacy'
On his government's Budget earlier this week, Mr Blair agreed the principle of making work pay and rewarding ambition was "Thatcher with a heart".
He also spoke of missing the freedom of his pre-Downing Street days, and said he seeks to reassure his three children by stressing he will not always be Prime Minister.
"I say to them: make your own life, do well, have your own ambition, work hard at school, discover who your real friends are and realise that you will be liberated from it at some stage."