The widow of Sen. Edward M. Kennedy told Oprah Winfrey in an interview broadcast Wednesday that even as her husband knew he was dying of brain cancer he had been "in training" to make sure he had enough strength to attend U.S. President Barack Obama's inauguration.

In the most extensive interview since her husband's death in August, Vicki Kennedy said she wouldn't try to run for her husband's former U.S. Senate seat and described how he battled brain cancer -- but she would not talk about the last thing he said to her before dying.

"I think I'll just keep that one to myself," she told Winfrey on "The Oprah Winfrey Show."

During the hour-long interview was taped Friday, Kennedy was sometimes joined on stage by her two grown children as well as Ted Kennedy Jr. She described her husband's seizure in May 2008, which led to his diagnosis of the brain cancer that ended his life at the age of 77.

"We went from thinking he had lost his life, to thinking that he'd had a stroke, to thinking that he wouldn't speak to thinking that he was OK, to then finding out that he might have a brain tumor all in the span of about three hours," she said.

She also told Winfrey about how her husband kept working on his book after his diagnosis and even was calling colleagues in the Senate to talk about strategy to push through legislation as he was traveling to Duke University Medical Center in Durham, N.C. to undergo brain surgery.

"It was an inspiration, really, to watch how Teddy grappled with such a grave diagnosis and always looked forward with hope," she said.

After watching a clip of her husband's speech at the Democratic National Convention, Kennedy said her husband, despite being told initially that he had just a few months to live, was determined to survive long enough to see Obama sworn in as president.

"He was in training to be there in January," she said. "He was exercising every single day to be strong enough to be there," and even calculated how many steps he would have to take that day.

During the interview, Winfrey held Ted Kennedy's memoir "True Compass," which was released shortly after Kennedy's death, and read from it a number of times. As of Tuesday, the book was 12th on the New York Times Best Sellers list for nonfiction titles.

Kennedy also adamantly told Winfrey that she had no intention of ever running for the Senate seat that her husband held for nearly a half century when the host mentioned about "talk" that she might run.

"No, no, not for me," she said. "We had Sen. Kennedy in our household."

The program also included clips from Kennedy's life. There was news coverage of assassinations of Ted Kennedy's older brothers, President John F. Kennedy and Sen. Robert F. Kennedy, along with Kennedy's own run failed run for president and the death of Mary Jo Kopechne, who drowned after Kennedy drove the car in which she was riding into a pond on Chappaquiddick island.

There were also scenes from Kennedy's funeral service -- including perhaps the most poignant moment during which in his eulogy of his father, Ted Kennedy Jr. told of having his leg amputated when he was 12 and how his father picked him up after he fell on a hill and told him that together they would "climb that hill together, if it takes us all day."

"He just gave me so much encouragement at a very difficult time in my life," Kennedy Jr. told Winfrey. "He was just such an optimistic person."

The younger Kennedy became emotional when he talked about a letter that his father wrote to Pope Benedict XVI after he was diagnosis of terminal brain cancer, a letter in which Kennedy acknowledged some of his failures and, as Winfrey read, how he had "tried to right my path."

"I though that was the most beautiful letter I've ever heard," he said.