Joan Mondale told more than 450 representatives of cultural and business groups at the Shoreham Hotel yesterday that support for the arts must come from private as well as government sectors.

"Federal subsidy is not a cure-all," the Vice President's wife said in her speech opening a two-day meeting. "The private sector must continue to invest in the arts . . . It is at the local level where artists are bred, audiences are formed and organization receive their mandate."

The meeting of cultural and civic group leaders from all 50 states was called to consider better management, financial and marketing methods for arts organization. The conference, the first such convocation, was called by Nancy Hanks, chairman of the National Endowment for the Arts, and Roger Stevens, chairman of the Kennedy Center.

Wearing a "Support the Arts" T-shirt, Hanks told the gathering in the Shoreham's Blue Room that arts endowments were too small and the cash reserve was non-existent.

She noted that the response to the Challange Grant Program, which provides matching funds on a one-time basis to assist arts instituations, had been overwhelming.

"Nearly 400 applicants seeking a total in excess of $130 million were received by the close of the first deadline in January, 1977," she said. "With a total of $9 million for Challenge Grants in fiscal 1977, and the prospect of $18 million for 1978, we decided to extend the challenge concepts beyond the grants program."

Thus the current meeting was called to determine how the Endowment could better serve the challenge goals and increase arts funding for local cultural groups.

Today's sessions, beginning at 9.15 a.m., will be held at the Kennedy Center.