The story of an American flyer, his grave on a Danish island in the North Sea and the couple who have kept it in flowers and U.S. flags since 1944 so touched President Reagan that he invited the couple to a White House dinner for Danish Prime Minister Poul Schlueter Tuesday night.

The White House said yesterday that Nels Mortensen, 86, a retired dentist, and his wife Natalia, 83, of Marstal, Denmark, subsequently sent their regrets. But among the evening's 120 guests will be the dead flyer's sister, Doris Woll, 59, and her husband, Robert, 68, of Willow Grove, Pa.

In a telephone interview yesterday, Doris Woll said Reagan first heard about the Mortensens and their care of her brother's grave when a friend of hers wrote the president earlier this summer.

"She said she told him, 'You shouldn't have gone to Bitburg but to Denmark.' She also told him about my brother's grave and how wonderful the Mortensens had been in caring for it all these years," Woll said.

Woll subsequently wrote Reagan at his request. About a week later he called her and they talked for almost 20 minutes. In that conversation, Woll said, Reagan told her how he once had represented President Nixon at the annual Danish-American Fourth of July celebration in Copenhagen.

"President Reagan told me that he had spoken to so many people and that one of the things he heard was how when the Germans occupied Denmark they issued a decree saying all Jews had to wear the Star of David starting the next day. That day not only Jews wore the star but so did everyone else," said Doris Woll.

Woll said her brother, Staff Sgt. Jack Wagner, 19 when he died, was a tail gunner on a B-25 bomber when it collided with another American Liberator over the North Sea in 1944. Wagner's body washed up on the shore near the Danish fishing village of Marstal where the townspeople found it July 11. They left his dogtags on his body but removed everything else that might provide their German occupiers with information that could hurt the Allied war effort.

The Germans buried him around 5 a.m. on July 12. Four hours later the Danes gave him a Christian burial. Published news accounts of the day said the turnout was massive and the floral tributes impressive, according to Woll, who visited her brother's grave for the first time two years ago.

That's when she and her husband met the Mortensens, who tend the grave once a week, put fresh flowers on it, keep it weeded and change the American flag there three or four times a year.

"A man at the cemetery drew us a map to the Mortensens' house," said Woll. "When we found it, Mr. Mortensen said his wife would be pleased to see us and when she walked in she said, 'Well, at last you've come.' It was as if she had been waiting for us all those years."

Woll said she received a letter from the Mortensens recently in which Natalia said because she had a heart attack last year, she was not strong enough to make the trip to Washington. "They've given up driving their car," said Woll, "but they still ride bicycles."

Others who have accepted the Reagans' invitation to dinner Tuesday night are designer Geoffrey Beane; entertainers Danny Kaye, Diahann Carroll, Telly Savalas, and Don Johnson and Philip Michael Thomas of "Miami Vice" stardom; CBS anchorman Dan Rather; National Football League commissioner Pete Rozelle; producer Robert Stigwood; and interior decorator Sister Parrish.

Weather permitting, dinner will be under the stars in the Rose Garden and entertainment on the South Lawn by singer Vic Damone.

"Normally, we've found that the early part of September is very, very safe because the thunderstorm period is over and it's usually not so humid," said departing White House social secretary Gahl Hodges. "But just in case, the number of guests will be the same as it would if the dinner were inside."

"The same way you do at home for a dinner outside," added Elaine Crispen, Nancy Reagan's press secretary, who will be making her debut in that capacity at the White House dinner.