An exhibition of more than 300 art works from Dresden, East Germany, originally scheduled to open at New York's Metropolitan Museum of Art, will instead be seen here first at the National Gallery of Art, it was learned yesterday.

The Dresden exhibition, which will open at the Gallery in May 1978, surveys one of Europe's richest art collections, that of the Dukes of Saxony. The show, the largest ever lent American museums by an Eastern European country, will include Renaissance suits of armor, jewelled statues, porcelains, drawings and paintings by such masters as Rembrandt, Titian, Velazquez, Holbem and van Dyke.

Gallery officials yesterday would not confirm they have scheduled the show, but officials at the State Department and at the Metropolitan acknowledged that its appearance here is set.

"They're touchy at the National Gallery, aren't they?" said Tomas P.F. Hoving, the Metropolitan's director. "They take the position they must get every exhibition first; if not, they'll take their ball away and play another game."

The Dresden show, which Hoving says "traces the history of collecting in Saxony, where art museums were born," is being organized by curators at the Metropolitan, as was the Egyptian Tut exhibit now on display here.

Arrangements for the show were initiated by David Rockefeller of the Chase Manhattan Bank during private conversations with officials of the German Democratic Republic in 1975. Shortly thereafter, Hoving and members of his staff visited Berlin to arrange the exhibition.

"When we announced the show last March," said Hoving, "officials at the Galley threw up their hands and said, 'but we had wanted it all along.'"

It is true that Gallery officials had previously been hoping for some sort of Dresden show. But their new building is unfinished, and as a semigovernment had been exchanged between East Germany and the United States, according to Hoving. That was done on Dec. 9, 1974. Sortly thereafter Hoving heard from Rockefeller that the German minister of culture was amenable to a Dresden exhibition. He then flew to Berlin.

The East Germans, like the Russians, the Chinese, the Egyptians and other governments whose relations with this country have occasionally been less than cordial, recognize the benefits of staging well-attended art shows in the United States. They had no objections to the Dresden show opening in Washington, and when J. Carter Brown, the Gallery's director, flew to Berlin to request a change of schedule, it was soon arranged.

Hoving said yesterday he will meet with Brown on Monday to discuss the details of the Dresden show, which remain unresolved. Both men will return to Germany in March.

The Gallery does not have curators who specialize in arms and armor, medieval ivories or the antiquities of Egypt, as does the more encyclopedic Metropolitan, and it is not as well equipped to organize such exhibits as the Tut or Dresden shows.

"Augustus of Saxony initiated the Dresden collections in the 16th century," complicated clocks, spheres-carved-within-spheres, Chinese porcelains, that sort of thing. And incredible armor. We hope to show two knights on horseback in full armor at the moment of impact in the joust. By the 19th century, Saxony's collections of jewels, arms and wonders had grown into a great museum of fine arts."

Many of Dresden's art works were destroyed during the firebombing of Feb. 13, 1945, but most were preserved in nearby salt mines. They are now owned by the East German state.

Hoving said the show will include a re-creation of the "Grunes Gewolbe" ("The Green Vault"), an 18th-century treasure room of gilded arches and green walls which he described as "the most beautiful museum installation in the world."