John Travolta shares how First Lady Nancy Reagan played a pivotal role in making one of Princess Diana's dreams come true

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When John Travolta took Princess Diana for a twirl around the dance floor, it was a dream come true — for her!

In an exclusive clip from the new special In Their Own Words: Diana, Princess of Wales, which premieres Sunday on PBS at 8 p.m. ET, the two-time Oscar nominee looks back on his famous partnering with the princess during a royal visit with President Ronald Reagan at the White House.

Travolta, now 67, shares that he "went with a very humble attitude" to the dinner because he felt he "was an extra in a room of very important people."

At the time of the dinner, the Princess of Wales was coming into her own as not just a royal but also a celebrity, says royal historian Kate Williams: "When Diana went to America in 1985, it cemented her place on a world stage. She was no longer this young, naive girl. She was a huge celebrity, the most famous woman in the world. Di-mania spread from Britain across the world, and then it seized the world."

Despite Travolta's professed role as an "extra" at the event, it wasn't long before one of the night's hosts approached him and asked him to take center stage.

Britain Fashion Diana Dresses, WASHINGTON, USA - 3 Jan 2005
From left: John Travolta and Princess Diana at the White House dinner
| Credit: AP/REX/Shutterstock

"About 10 o'clock at night, Nancy Reagan tapped on my shoulder and said, 'The princess, her fantasy is to dance with you. Would you like to dance with her tonight?'" he recalls. "And I said, 'Well of course.'"

The First Lady explained that she would escort Travolta over to Diana around midnight so he could ask her to dance.

When his big moment arrived, Travolta recalls, "My heart starts to race, you know, and I tap her on the shoulder and she turns around and looks at me, and she had that kind of bashful dip [of her chin] that she did, and she looked up at me, and I said, 'Would you care to dance with me?'"

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John Travolta and Princess Diana
| Credit: corbis/Getty Images

"The whole room cleared," says Travolta. And the rest went down in royals and Hollywood history. "We danced for what felt like 15 minutes."

A photographer captured the pair in action, with Diana looking anything but bashful next to the Saturday Night Fever star.

According the princess's astrologer Debbie Frank, Diana "loved dancing, and she brought pure joy to everyone else."

"It was a storybook moment," says Travolta. "We bowed when it was over, and, you know, she was off, and I was off, and my carriage turned into a pumpkin."

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In Their Own Words: Diana, Princess of Wales premieres Sunday at 8 p.m. ET on PBS.