The National Symphony Orchestra will receive $1 million from the National Endowment for the Arts in the first round of "challenge" grants that could generate upward to $200 million in new money for the arts.

The arts endowment announced yesterday that $27 million will go to 59 grantees chosen from nearly 400 applicants.

The institutions must raise at least $3 in new money for each $1 of federal subsidy. Actually, the grantees projected raising money than $180 million in matching funds - almost a 6-to-1 basis.

The challenge-grant program was designed to do just that: to provide seed money to generate new funds to insure financial stability and independence for institutions that often have to cry "emergency" each new season.

The grants were announced yesterday before President Carter actually had gotten around to signing the appropriations bill that provides the money. He is expected to sign today or the legislation will become effective anyway in the absence of a veto.

The National Symphony, one of 11 orchestras nationally to receive the initial challenge grants, is the only recipient from the District.

It wad double good news for the National Symphony, which announced yesterday it also will receive $350,000 from the Andrew W. Mellon Foundation. This also comes on a 3-to-1 matching basis.

"The challenge grant is the single most important thing that has happened to us in quite a bit of time," said Oleg Lobanov, the symphony's managing director.

The National Symphony, with an annual operating budget of about $4 1/2 million, has a permanent endowment of $5 million. Lobanov said the challenge and Mellon grants will be the "cornerstone" of a drive to raise the endowment to at least $9 million. Even then, he emphasized, the National Symphony lags behind other orchestras of its stature, with some having up to $20-million endowments to provide financial stability.

Symphony sponsors now have the challenge of raising $4 million is new money over the next three years. That will be in addition to the fund appeals for annual operating expenses. "This year $1.4 million was raised.

Challenge grants are made on a one-time basis. The idea is to build a strong, reliable annual funding base and efficient business management to avoid financial brinksmanship each new season. There have been some fears that the challenge grant program might divert too much energy and attention to raising money. But its supporters argue it will free institutions from immediate money worries so they can get about the creative business of the arts.

For Atlanta Landmarks, Inc./Fox Theater in Atlanta, the $300,000 challenge grant announced yesterday could mean survival.

The Fox Theater, a national historic landmark operating as a performing arts center, has been threatened with demolition next June if the mortgage isn't paid.

The first round of $27 million in challenge grants comes from a $9-million supplemental appropriation for last fiscal year and $18 million this year. The three-year program calls for $20 million next fiscal year.

Nancy Hanks, chairman of the arts endowment, pointed out that the nearly 400 grant applications requesting $130 million reflect "the vitality of the nation's art organizations and their commitment to community service." Only 15 per cent could be funded in the first round of challenge grants, but she noted that the program has strong congressional and White House backing.

The biggest individual grant announced yesterday went to the Metropolitan Opera Assn., which teeters on financial bankruptcy each season. It received $1.5 million to launch a five-year endowment campaign and to help meet increased operating costs.

A Los Angeles consortium received $2,04 million for the Center Theater Group/Mark Taper Forum, the Los Angeles Master Chorale, and the Los Angeles Philharmonic.

The list of grants includes:

American Conservatory Theater Foundation, $400,000; Art Institute of Chicago, $500,000; The Arts Alliance, Inc., $500,000; Atlanta Landmarks, Inc./Council, Inc. Winston-Salem, $700,00; Atlanta Arts Fox Theater, $300,000; Baltimore Museum of Art, 3800 000: Baltimore Symphony Orchestra Assn., $600,000: Brooklyn Academy of Music, $350,000: Brooklyn Institute of Arts and Sciences, $1 million; Carnegie Institute and the Pittsburgh Symphony Society, $2 million. The Chicago Theater Group, $200,000.

The City Center of Music and Drama, New York., $1 million; Columbus Assn. for the Performing Arts, $350,000: Connecticut Players Foundation, $100,000: Craft and Folia Art Museum, Los Angeles, $100,000: Dallas Museum of Fine Arts., $75,000: Denver Art Museum, $75, 000: Foundation for the Joffrey Ballet, $450,000.

Founders Society, Detroit Institute of the Arts, $750,000: Global Village Video Resources Center. New York $80,000: Greater St. Louis Arts and Foundation Council, $250,000: Group 1 Acting Company, New York, $60,000: Hartford Stage Company $700,000: Henry Street Settlement, New York $25,000: Houston Grand Opera Assn., $500,000: Lincoln Center for the Performing Arts, $500,000: Lyric Opera of Chicago, $600,000.

Martha Graham Center for Contemprary Opera $250,000; Metropolitan Museum of Arts Metropolitan Opera Assn. $1.5 million Minnesota Opera Company, $150,000: The Museum of Moorin Art, $1 million: Museum of Science. Episton, $4.000: Musical Arts Assn Orchestra. Cleveland $1 million: Nashville Symphony Assn., $100,000; National Symphony, Orchestra Washington $1 million: New York Landmarks Conservatory, $45,000.

Oregon Symphony Society, $100,000: The Palace of Arts and Sciences Foundation. San Francisco, $60,000: Performing Arts Council of the Music Center of Los Angeles, $2.04 million: Puerto Rican Traveling Theater Company, $800,000: Rhode Island School of Design, $50,000: Richmond Symphony, $50,000: St. Louis Symphony Society, $1 million; Seattle Symphony Orchestra. $600,000; Settlement Music School of Philadelphia, $100,000: South Coast Repertory, Costa Viesa, Calif., $30,000; Sponsors of the San Francisco PerformingArts Center, Ind., $1 million: Trinity Personna Company Trinity Square Repertory Theater, Providence, R.I., $40,000.

Tayla Tharp Dance Foundation, New York. $50,000 Urban Gateway. Chicago, $60,000; Utah Symphony Orchestra, $365,000: Volunteer Lawyers for the Arts, New york, $42,000 WGSH Educational Foundation, Boston, $375,000.