Gluck’s operas are filled with music written especially for dance, particularly the versions prepared for production in Paris. But in the Metropolitan Opera’s new production of Gluck’s “Orfeo ed Euridice,” which had its premiere Wednesday night, dance, though courtesy of Mark Morris, was the production’s weakest element. Or perhaps weak is not the right word — extraneous might be more like it.

There was glorious singing and instrumental playing under the baton of James Levine. And there was coherent staging by Mr. Morris, who has previously staged the opera in Seattle. But Mr. Morris’s choreography and the participation of virtually the entirety of his dance company added little to the production.

The Met’s new production is influenced by, or cognizant of, earlier cinematic treatments of the tale, namely Jean Cocteau’s 1950 film and the 1959 “Black Orpheus,” set in the Brazilian Carnival.

In 1936, Balanchine choreographed a Met production of “Orfeo” that put all the singers, chorus, and leads in the pit, while his dancers performed the onstage action. Like Balanchine, Mr. Morris has used his own dance company, augmented by four dancers from the Met’s own troupe, but here the singing leads are integral to the action, while the chorus stays seated or sometimes standing in Allen Moyer’s grey amphitheater tiers.

Mr. Morris’s dancers are sometimes used to assist in the narrative action or comment or illustrate the libretto. They interact with the singers, and there is occasional unanimity between chorus and dancers. And at these times they blend into the actions. When the dancers are center stage, however, one couldn’t help wonder what they were doing in the production. The choreography is almost completely drained of Baroque tint, even when Mr. Morris uses a soft-edged dialect of the language of ballet, itself a child of the Baroque.

Musically, Mr. Morris and Gluck are not a perfect fit, because of the choreographer’s preference for responding to notes as much as phrases; this approach tends to fracture Gluck’s long-breathed melodic line with a gratuitous amount of ticks and twitches. Dance doesn’t have to conform to its musical partners, and there can be welcome tension in opposition. But here there is no question that Gluck is dominant and is to be ignored at a choreographer’s peril. Perhaps it’s a question of context: What would be welcome on Mr. Morris’s own stage becomes intrusive in this environment.

This was particularly true during the finale, where the magnificent music and choral singing dwarfed the set pieces performed by the Morris company. In these closing celebratory dances, which follow the restoration of Euridice to Orfeo, Mr. Morris has taken the post-modern prerogative of conforming to a hallowed score only by observing the phrase lengths and rhythms. There are dips and twirls suggesting pop dances of the 1940s such as the Lindy, as well as the stomping accompaniments of a hoedown.

Mr. Morris’s direction demonstrated his solid staging abilities, especially in the first scene in which Orfeo repeatedly runs to the front of the stage as he appeals for succor from his grief. Countertenor David Daniels interpreted the role as a mensch whose frustration and bereavement are conveyed with a pleading, almost adolescent urgency, and this made for an effective contrast to his voice’s high register.

Mr. Moyer’s set design is stylishly timeless. An earth-toned elliptical wall, stippled to let stars shine through at times, encloses the tiers occupied by the chorus. The cylinder is closed by an enormous, appropriately black link when Mr. Daniels and Maija Kovalevska as Euridice make their fraught ascent out of Hades, hewing a path cut into what suggests a mountain peak or outcropping (an improvement over a similar piece in Mr. Moyer’s design for Mr. Morris’s “Sylvia,” seen in New York last summer). Here the large, resonant, eloquent voices of Mr. Daniels and Ms. Kovalevska took you into the score’s essentials and dwarfed any other consideration.