Mstislav Rostropovich and the National Symphony left for their month-long tour of Europe yesterday afternoon with orchestra tote bags full of products by Amway Corp., the tour sponsor, and a personal farewell from Nancy Reagan, who went to the Kennedy Center to see them off.

There was a special gift for Rostropovich from Mrs. Reagan. His unwrapping it in the chilly breeze in front of the Kennedy Center, with the orchestra and a crowd of about 100 well-wishers standing around, gave the television people something to photograph. Ever the showman, Rostropovich rose to the occasion. The white package was wrapped with a heavy red ribbon sealed with a gold paper medallion that had a lot of gummy glue on the back. Rostropovich pulled it off and stuck it to his left lapel in the manner of great medals. Then, while he continued unwrapping, Mrs. Reagan draped the red ribbon ceremonially around his neck.

Inside the package was a heavy-duty sweat shirt emblazoned in red on the front with "National Symphony Orchestra Tour," and, on the back, "If lost please return to Washington, D.C." But even with Rostropovich's newly svelte figure, it would be surprising to see him jogging in it.

He responded to the gift in true style, with hugs for Mrs. Reagan, kisses on each cheek and kisses of the hand.

The cliffhanger of the departure turned out to involve Rostropovich. He had gone to Upstate New York for the weekend and woke up yesterday morning to find that his commercial flight from Utica had been canceled because of snow. So the National Symphony had to send a small jet to bring him back.

The first concert will be in Zurich Thursday and there will be 17 concerts in 16 cities between then and Feb. 25, when the tour is to end in Madrid. Such major musical centers as Berlin, Vienna, Paris and London will be included.

Another farewell event yesterday was a luncheon at the Watergate hosted by Amway. Mayor Marion Barry spoke, declaring yesterday National Symphony Orchestra Day. Amway president Rich DeVos, who is also finance chairman of the Republican National Committee, presented a portrait of Rostropovich by artist Paul Collins, who is from Amway's base of Grand Rapids, Mich., and followed it with a tribute to Rostropovich, whom he described as "a man with a mission, a man who discovered the joy of freedom, and perhaps the best ambassador that ever would be."