THE JAPANESE people know what is true beauty," Mstislav Rostropovich said at his first press conference in Osaka. And he repeated the theme, with variations, a dozen times during his tour of Japan and Korea with the National Symphony Orchestra, which ended Friday.

At his Tokyo press conference, he was more personal about it: "Musically, the Japanese understand everything I try to say. Everyone understands Tchaikovsky, and the Japanese do, too -- but they also understand Shostakovich and Prokofiev, and that is not so easy. I think audiences in Japan are not lazy."

They certainly were not lazy during the NSO's tour of Japan. The applause was energetic in the extreme -- loud and prolonged through encore after encore. The orchestra was deluged with flowers, and long lines of fans -- largely college-age -- waited patiently at the stage door for autographs. In some cities, they even lined the streets, waving and cheering, as the buses carrying the orchestra drove away from the concert hall.

The orchestra responded to the audience's affection and justified it with some extraordinary performances. "You can feel it when the audience is with you," said double bassist Donald Havas, summing up a consensus opinion. "That comes across to you very quickly after you start playing, and naturally you respond to the feeling you are getting from the audience. It's been very good on this trip."

Sometimes, the response may have been a shade better than the orchestra deserved. At its best -- in the music of Shostakovich and Prokofiev and sometimes of Tchaikovsky -- the National Symphony in Japan was an orchestra of international caliber, delivering powerful, distinctive and techinically expert performances. Its Beethoven was less distinctive but generaly quite good. The interpretations did not have the mark of Rostropovich's personality as the Russian selections did, but they were solid, straightforward readings, generally reliable and often exciting.

The First Piano Concerto of Brahms was the problematic work on the tour programs, and the problem was primarily that of the conductor and soloist Alexis Weissenberg rather than the orchestra. Rostropovich simply has not lived with the music long enough yet to be sure what he wants to do with it. But in terms of perceptible growth, his handling of this music was his most impressive performance on the tour. Each time the concerto was played, the conductor had made a perceptible advance beyond his previous interpretation. There was still room for significant improvement after his final performance, but in his handling of the Brahms, Rostropovich showed once again that he is a great musician and potentially a great conductor. As a cellist and as a conductor of Shostakovich, Rostropovich exemplifies one kind of greatness: the ability to do difficult things impressively and with ease. As a conductor of unfamiliar repertoire like the Brahms, he shows a more impressive potential: the ability humbly to recognize his weaknesses, to work on them sytematically and to overcome them. Paradoxicaly, it was precisely his problems on this tour and the way he approached them that gave the greatest hope of Rostropovich's development as a conductor. On the evidence of this tour, it may be said that he is still in the early stages of a growth that may be unlimited. A landmark will be passed when his Brahms is as good as his Shostakovich, and that day is coming.

The National Symphony would not have been invited to the Osaka Festival if its conductor had not been Mstislav Rostropovich. He secured the invitation, as he has secured the services of some superstar guest conductors, through a kind of polite blackmail, trading on his international stature as a cellist. "When they invited me to come to Japan with my cello," he admitted in a private conversation, "I told them, 'First I come with my orchestra.'" True to his word, he will be returning to Japan as a soloist next month.

Although not all of them are aware of this particular quid pro quo, the orchestra's members recognize that their conductor's status has given them a special prestige. Many of them are more familiar than he with the basic Viennese orchestral repertoire, but they talk about him without the kind of condescension that is often heard when orchestra members discuss conductors. There is sometimes disagreement on points of interpretation, occasionally a bit of insecurity about his cues (although he is credited with a beat easier to follow than that of Antal Dorati), but generally the feeling is one of respect, tinged with the hope that this may be the conductor who will take the orcehstra to the top.

On tour as in the Kennedy Center, performances under Rostropovich were highly variable, reflecting the conductor's strengths and weaknesses. The ensemble sound seemed to improve steadily in most repertoire during the first two weeks of the tour, then fell off a bit from its peak in the third Tokyo performance -- perhaps because of travel fatigue, perhaps because some of the pieces were being played once too often.

But the basic motif of the tour was solid growth. It could be heard, from one concert to the next, by those who traveled with the orchestra; it was most spectacular in Russian repertoire, but steady in the Viennese.When the orchestra was at its peak, it did not seem strange to see its name listed among those of other foreign orchestras visiting Japan currently or in the near future -- a distinguished group that includes the London Symphony, the Orchestre de Paris and the Vienna Philharmonic. It did not always maintain that level, but it showed what it can do and it set a standard for the musicians to keep in mind for the future.

Tomorrow, the orchestra returns to business as usual at the Kennedy Center -- except that the business is hardly usual: two long rehearsals of Mahler's monumental Eighth Symphony under Erich Leinsdorf. This is a tremendous challenge for any orchestra and especially for one with only two days of rest after a three-week tour on the other side of the world.

If the NSO can preserve the momentum gained on its tour -- if it can show its Washington audience regularly the kind of incandescence it reached during its finest moments in Japan, this expedition may prove to be a turning point in its history.