Late yesterday afternoon in the East Room of the White House, President Reagan got Beverly Sills to do what no one else has succeeded in doing: He persuaded her to sing publicly, before a microphone, for the first time since her retirement from the opera stage more than a year ago.

It happened at the end of the second in a series of concerts in which young American artists receive the cachet of being presented in the White House and over television, with Sills as mistress of ceremonies. For more than half an hour, Sills had introduced eight of the stars of her New York City Opera who sang arias and duets from opera and operetta. When it was over, the president said, "I speak for all of you when I say the singing we have heard today was beautiful. Is there anything more beautiful than the human voice when it is done like that?"

Then, turning to Sills, he asked if she would make an exception to her self-imposed rule of not singing publicly and lead everyone in some Christmas songs. And she did. With her young stars and an ensemble of Marine band musicians, she sang "Jingle Bells," and it was a lovely thing to hear that voice again. There was something so persuasive in her manner and appearance that, after the soloists had sung "Joy to the World" and "O Holy Night," everyone sang "O Come All Ye Faithful."

The East Room was full of Christmas beauty for the program that was shown later last night on television. Against a background of six lighted Christmas trees, with great red candles gleaming in hurricane lanterns, and clusters of poinsettias, Sills introduced sopranos Ashley Putnam, Carol Vaness and Gianni Rolandi, mezzo Gail Gilmore, tenors Vinson Cole and Barry McCauley and baritones Stephen Dickson and Alan Titus. Donald Hassard was an indefatigable pianist for everything from the "Rigoletto" Quartet to Leonard Bernstein's "Glitter and Be Gay." William Huckaby played the glockenspiel for one of Papageno's arias from "The Magic Flute" with such irresistible charm that it sounded as if Mozart had meant it to be played just for Christmas.

At the outset, Nancy Reagan introduced Sills and her stars, saying, "We are going to hear voices that sparkle as brilliantly as the lights on those trees."

The young singers performed for an invited audience that included Chief Justice and Mrs. Warren Burger and Secretary of Defense Caspar Weinberger, and from the world of music, Zubin Mehta, the music director of the New York Philharmonic Orchestra. When it was over, everyone adjourned to the State Dining Room for a party.