LONDON (AP) _ Queen Elizabeth II, speaking from the heart as ``your queen and as a grandmother,'' paid tribute today to Princess Diana as an ``exceptional and gifted human being.''

She spoke hours after people in the streets had reached out directly to Diana's sons, Prince William and Prince Harry, and to her and Prince Charles, outside the palaces which have been a focus for an immense public tribute.

``We have all been trying in our different ways to cope,'' the queen said in her first live broadcast to her subjects in 40 years.

``It is not easy to express a sense of loss, since the initial shock is often succeeded by a mixture of other feelings: disbelief, incomprehension, anger _ and concern for those who remain.''

The queen normally speaks to the nation only on Christmas Day. This was the second exception in her 45-year reign; the other was on Feb. 24, 1991, at the end of the Gulf War.

Many people felt the royal family had treated Prince Charles' ex-wife badly, culminating in the stripping of her title of Her Royal Highness after the divorce last year.

``I want to pay tribute to Diana myself. She was an exceptional and gifted human being. In good times and bad, she never lost her capacity to smile and laugh, nor to inspire others with her warmth and kindness,'' the queen said.

``I admired and respected her _ for her energy and commitment to others, and especially for her devotion to her two boys,'' she said.

She also responded to criticism that the royal family had been aloof during this week while they were secluded at Balmoral Castle in Scotland.

``We have all been trying to help William and Harry come to terms with the devastating loss that they and the rest of us have suffered,'' she said.

Speaking steadily through one of the most testing times of her reign, the queen said, ``We have seen, throughout Britain and around the world, an overwhelming expression of sadness at Diana's death.

``We have all felt those emotions in these last few days. So what I say to you now, as your queen and as a grandmother, I say from my heart.''

``I hope that tomorrow we can all, wherever we are, join in expressing our grief at Diana's loss, and gratitude for her all-too-short life,'' the queen said. ``It is a chance to show to the whole world the British nation united in grief and respect.''

Earlier today, the queen, wearing black, arrived from Scotland and went to Buckingham Palace. Stepping from her limousine, she spoke with some of the thousands who gathered to offer condolences, shaking hands and smiling bravely as she accepted their flowers.

The queen also met other mourners outside the Chapel Royal at St. James's Palace and paid her respects at Diana's coffin.

Her public presence, along with the broadcast, seemed to mollify some Britons waiting outside Westminster Abbey, site of Diana's funeral Saturday.

``I think it was about time. We've been ignored in our grief,'' said Yvonne Titman of London.

``She's in a difficult position, isn't she?'' Titman said. ``She's queen of our country, and she has a lot of protocol to follow. But we must not confuse protocol with her personal feelings. We needed direction, and that's what she gave us.''

Said Eileen Connell of Cumbria, in northwest England, also at the abbey, ``She definitely sounded sincere. She made us feel as we are all as one.''

With solemn faces and shy smiles of thanks, Diana's young sons came face-to-face today with people outside Kensington Palace, Diana's former residence.

William, 15, tall and bearing a striking resemblance to his mother, walked with his father, Prince Charles, and brother, Prince Harry, 12, near the railings of the palace, examining a sea of floral tributes.

Britons appeared deeply touched by their appearances.

``Prince Charles said to me, `We appreciate you coming, we appreciate all the flowers, we are very touched,''' said Rosalind Wederell, from Chatham, who was at the front of the police barrier at Kensington.

Charles gulped several times before making a remark to the boys, and William looked moist-eyed. But the young princes conducted themselves in an assured way.

``Prince Charles seemed overwhelmed and somehow a lot more human than he ever seemed to be before. I said to William, `You are a wonderful boy,' and he smiled at me,'' Wederell said.

Londoner Andy Kalli said William thanked him. ``I said to him, `Be strong, your mum is in a good place,' and he smiled.''

Meanwhile, the family of Diana's new love, Dodi Fayed, said today that Diana had given him a pair of cuff links that belonged to her late father and a gold cigar clipper with a tag inscribed ``With love from Diana.''

The family also confirmed reports that Fayed gave Diana a $205,000 diamond solitaire ring shortly before they were both killed in a car crash early Sunday in Paris.

``What that ring meant, we shall probably never know,'' said Michael Cole, spokesman for Fayed's father, Egyptian-born billionaire Mohamed Al Fayed.

Cole also showed reporters a security video containing shots of Diana and Dodi's last hours at the Ritz Hotel in Paris.

The video showed Diana waiting inside the hotel's rear entrance, Dodi's arm around her waist. When the Mercedes Benz limo arrived, they got in the back seat and the limo drove off slowly.

Footage from a security camera at the front of the hotel showed a posse of figures then racing toward motorcycles.

The Fayed family released the video to counter reports that Diana's driver, Henri Paul, had raced off at high speeds. French police say Paul was legally drunk at the time of the crash.

With the funeral approaching, there has been no letup in the public surge of emotion. Police estimated that 12,000 people were in line today _ a 10-hour wait_ to sign condolence books at St. James's Palace.

Diana will be buried privately after a public procession and a Westminster Abbey funeral that will blend Anglican funeral rites with a song by Elton John. The procession and funeral will be broadcast on three giant TV screens in London _ two in Hyde Park and one in Regent's Park_ as well as around the world.

Diana's brother, the ninth Earl Spencer, announced today that his sister will be buried on an island on the grounds of the family's stately home, Althorp Park, instead of in the nearby church. The change was made so the village of Great Brington would not be turned into a shrine to the 36-year-old Diana.

French police, meanwhile, held three more photographers in their investigation of the Paris crash. Earlier, seven photographers and a motorcyclist were detained.

The paparazzi could be charged with manslaughter and other crimes. All of those detained have denied claims that the high-speed pursuit of Diana's car caused the wreck that took her life.

Authorities are particularly interested in how one photographer's car came to be parked in front of Diana's crumpled Mercedes inside the tunnel.