From its earliest days, when the pianist Jelly Roll Morton spoke of a “Spanish tinge,” jazz has been extraordinarily open to international influences. Now it’s official. Last fall Unesco — the United Nations Educational, Scientific and Cultural Organization — designated jazz a “universal music of freedom and creativity” and decreed that henceforth every April 30 is to be celebrated around the world as International Jazz Day.


As part of the first year’s festivities — and also to show jazz’s global reach — some of the genre’s biggest names will be performing on Monday night at the United Nations headquarters, in the same space where world leaders gather each fall for the General Assembly. In addition to American players like Herbie Hancock, Wayne Shorter, Stevie Wonder, Wynton Marsalis and Esperanza Spalding, musicians from Latin America, Africa, Europe and Asia will also be participating.


On Sunday afternoon, after a custom-made stage had been installed directly under the United Nations emblem in the assembly hall, the musicians began arriving to rehearse the songs they plan to play. After one pick-up all-star ensemble worked its way through a Latin jazz set, another, featuring Mr. Wonder and Ms. Spalding on vocals, grappled with a lilting bossa-nova-flavored version of the standard “Midnight Sun,” most closely associated with Ella Fitzgerald.


“Maybe you could go to a G7th chord there,” Mr. Wonder suggested to one of the other musicians after the lead-in to his harmonica solo. “We need something different there.”


Observing off to the side was the actor Robert De Niro, one of the presenters of the event along with Michael Douglas and Morgan Freeman.


Out in the audience, tapping their feet as they waited their turn to rehearse, were two African performers: the brass player Hugh Masekela of South Africa and the guitarist Lionel Loueke of Benin.


“Jazz is a great music that I feel has never been given its just due or recognition for having affected so many lives in various cultures throughout the world,” said Mr. Hancock, who was the driving force behind the designation and is a special ambassador for the organization. “Unesco is exactly the proper setting to do that. With these musicians from various nations, we’re really showing a vision for globalization that’s a positive one.”


Monday night’s concert follows similar shows on Friday night in Paris, once a home to expatriate American players like Dexter Gordon, Sidney Bechet, Bud Powell and Archie Shepp; and at sunrise Monday morning in New Orleans, considered the birthplace of jazz. Scheduled to attend all three events is Irina Bokova, a former Bulgarian minister of foreign affairs, who is now director general of Unesco.


“I think there is a lot of symbolism around jazz and the multiculturalism and diversity of which it speaks,” she said in a telephone interview from Paris. “If you ask what jazz is for me, I’d say it’s freedom, human dignity and boundless spirit, which makes it a very very powerful universal force. We say around here that jazz was born in the United States, but is owned by the world.”


Several of the foreign-born musicians playing on Monday’s program echoed those sentiments, saying that they were originally drawn to jazz by its spontaneity, which they associate with personal freedom. The Japanese pianist Hiromi Uehara said that she had originally set out to be a classical pianist but changed course when she heard records by Erroll Garner and Oscar Peterson in her piano teacher’s collection.


“I was 8 back then, and my teacher explained to me that it’s all improvised, just like conversation, and that was my favorite part, that I felt this very elastic quality that changed every day,” said Ms. Uehara, who is now 33 and has recorded a duet CD with Chick Corea. “Because jazz is such an improvised music, you can really show and expose yourself, and that is what I love most about playing it even now.”


Halfway around the world, in Panama, the pianist Danilo Pérez, a member of Mr. Shorter’s quartet for more than a decade, had a similar reaction when first exposed to jazz. Hearing improvised solos on records by Louis Armstrong, Freddie Hubbard and George Benson “connected me to a sound of originality and freedom, of having a personal voice,” he said.


“What jazz brings to the table is collective improvisation and tolerance, respect and freedom, and when you mix that up with every world musical style, you are creating a cultural passport,” he added. “I really believe that what jazz has given to the world is a window, a paradigm of how countries should be interacting with each other.”