The National Endowment for the Arts has announced it will start a pilot program of giving grants to local arts agencies around the country. The program will start a year from now -- at the beginning of fiscal 1984 -- with a budget of $1 million to $2 million depending on the total NEA budget.

The NEA presented the program to the National Council on the Arts at its quarterly round of meetings here Friday and Saturday. Under the plan, 10 to 15 grants of at least $150,000 each would be awarded the first year either to local arts agencies or to state agencies for them to concentrate on local arts agencies.

The local arts agency must match the grant two-to-one with local government funds. The grants could be used for touring programs or other services for local arts groups or for regranting to local arts groups. In that case, the local arts agency must show how it sets up a review system to award the grants.

By law, the NEA must set aside a certain percentage of its budget for block grants to all the state arts agencies. But the NEA has never awarded such grants directly to municipal or city arts agencies. (In Washington, the D.C. Commission on the Arts functions as a state arts agency.)

"I think the new program will try to encourage a wider base of support for the arts at the local level, particularly from local governments," said Anthony Turney, deputy to the NEA chairman for public partnership.

The council of presidentially appointed advisers to the NEA approved the plan, but some members had reservations.

"I have grave concerns about starting these kinds of programs now," said council member Rosalind Wyman. "Every time we turn around, we're starting a new program and we're taking money out of other existing NEA programs . . . Where's the money coming from?"

According to NEA chairman Frank Hodsoll, the money is coming from other programs. "We shaved a lot of programs," he said, but only from places where there was excess. Hodsoll said that he and other NEA officials found about $11 million -- "a pot of money which one could argue wouldn't have to go back to the programs."

Hodsoll said the funds could be "be shifted without major problems." The NEA has spread those funds over the new local arts agencies program, the special-projects program, and the challenge grant program.