A $20 million endowment drive meant to end "chaotic and chronic" budget problems plaguing the National Symphony Orchestra was announced yesterday.

More than half the money -- $10.4 million -- has already been pledged, said Virginia C. Mars, the president of the orchestra's board, during a news conference at the Kennedy Center.

The $20 million would nearly quadruple the orchestra's current endowment of $5.6 million and is intended to give the NSO permanent protection from the almost annual budget crises that have struck it since its founding in 1931.

To launch the drive, Mars said, the orchestra's 85-member board has pledged $9.02 million, which is believed to be the largest amount ever raised in a single effort by a symphony orchestra's board of directors.

In addition, the National Endowment for the Arts has awarded the NSO a $900,000 challenge grant, to be matched 3 to 1. Also, two pledges of $125,000 each have been received from two of the orchestra's 53 national trustees.

A letter to the board from President Reagan was read; it congratulated the board members on the fund drive and paid tribute to music director Mstislav Rostropovich, who was also on hand for the announcement.

NSO financing has been particularly hamstrung by two problems that are more acute here than in other important orchestras.

One is the absence of regular and substantial state, county and local support -- a result of the peculiar relationship over the years between the federal and D.C. governments.

The other problem has been the modesty of the orchestra's endowment by comparison with other orchestras -- for example, the Pittsburgh Symphony ($43 million); the New York Philharmonic ($29 million); or the Philadelphia Orchestra ($24 million). This results partly from the lack of a major industrial base for the metropolitan Washington economy.

NSO executive director Henry Fogel said the endowment drive, which is targeted to end within two years, should "remove the atmosphere of crisis and put the National Symphony on a firm financial footing by comparison with other orchestras."

The initial goal, he said, "is to have the budget balanced and most of the accumulated deficit retired" by the season of 1988-89.

"And even then," he added, "we will have to keep going on raising for the endowment if we're not back into trouble in another 10 years."

The drive was launched, said Mars, with a $1.5 million gift from Austin H. Kiplinger and the Kiplinger Foundation. In brief remarks, Kiplinger said, "now that musical distinction has been achieved, now we must have a financial foundation . . . a great orchestra now exists and nothing else will be acceptable again."

There were also $1 million challange grants from Carl M. Freeman, board chairman of Carl M. Freeman Associates, and David Lloyd Kreeger, honorary chairman of the Government Employees Insurance Co. Mars also noted "major gifts and key leadership" from Norman Bernstein, president of Norman Bernstein Management Inc.; June Hechinger, trustee of the Hechinger Foundation; and Henry Strong, president and board chairman of the Hattie M. Strong Foundation.

The $10.4 million already pledged has allowed the orchestra to begin retiring its current $3.7 million debt.

The current NSO annual budget is approximately $12 million, about 80 percent of which is "artistic related," said Fogel. "That includes guest soloists, guest conductors, resident conductors, players 104 , and hall rental, etc."

Current revenues are as follows: earned income, 46 percent; endowment income, 6 percent; income from contributors, 28 percent; grants, 5 percent. That leaves 15 percent to be raised from other sources. The shortfall came despite a 28 percent increase in earned income in the last two fiscal years; expense controls that limited the increase in spending to 6 percent in the same period; a wage freeze agreement between musicians and management in 1982; and a $2 million line of credit from American Security Bank.

Among the financial efforts planned to complete the endowment fund are a $2 million drive by the National Trustees, another $2 million drive directed at area leaders and businesses, and a national corporate campaign drive.