The New York City Opera's director, Beverly Sills, today questioned whether the opera company will survive its bitter, 6-week-old labor dispute with its orchestra.

"I am seriously concerned about the future existence of the NYCO," Sills said in a prepared statement.

John Glasel, president of Local 802 of the American Federation of Musicians, responded, "So are we."

Sills refused any comment beyond the statement. But in it, she called the orchestra's demands "frankly, off the wall."

She charged that "the union's present position appears to be aimed at killing our summer season." She called for arbitration of the labor dispute and noted that the orchestra already has rejected this potential solution.

The musicians are seeking restoration of a portion of what the opera company says are 16 discontinued annual work weeks, vacation weeks and supplementary-unemployment-benefit weeks. They also are seeking salary increases and a reduction of one-sixth of their weekly workload.

The orchestra, which has been without a contract for a year, struck the NYCO July 6--the night before the company was scheduled to begin its new summer-autumn season of 19 weeks.

Orchestra spokesmen this week charged that the NYCO, in unilaterally reducing the orchestra's weeks of compensation by about one-third without consulting the musicians, had brought about the strike as an excuse to cancel the company's 1983 season, which had an exceptionally small advance sale.

Meanwhile, the opera company's founder and first music director and chief conductor, Laszlo Halasz, has agreed to conduct a free strike concert with orchestra members Sept. 1 at Lincoln Center and has called for the NYCO to file for bankruptcy, reform and move itself out of the Lincoln Center complex. The orchestra earlier announced it is arranging a special benefit cocktail party to secure major new donors for the opera company, in an attempt to improve the beleaguered company's financial picture.