The First Lady invited the royal pair to a dinner dance as part of their visit. Among the other guests at the prestigious event were movie stars John Travolta, Clint Eastwood and Tom Selleck.
At one point during the night, John Travolta asked Princess Diana for a dance and the spotlight turned to them.
"After the royals and the Reagans had danced the first dance, the First Lady approached Travolta. ‘It’s time now, John,' she said," Kelley wrote.
"The movie star walked over to the Princess’s table and asked her to dance. ‘I was thrilled.’ Diana said.
"Everybody stopped talking to watch them and completely ignored the Prince of Wales, who was dancing with the ballerina Suzanne Farrell."
The Grease star spoke about their special moment together.
"She had great rhythm. We did spins and turns. We did a kind of modern fox-trot, and she followed me very well. She’s a good little mover," he recalled.
But it wasn't long before she turned her attention to Clint Eastwood and the pair ended up taking a turn on the dance floor.
Afterwards, Eastwood commented it has "made his day".