The chairman of the National Endowment for the Arts yesterday predicted that budget cuts proposed for his agency would have only marginal impact on the nation's artists and warned arts lobbying groups to be realistic in their expectations for government funding.

"Our budget is a part of the economy. I would urge you to bear that in mind in your advocacy . . . so that you retain your credibility," endowment chairman Francis S.M. Hodsoll told members of Opera America, a trade organization of the nation's professional opera companies. Representatives of those companies met in Washington this week.

Hodsoll's remarks came on the same day President Reagan presented his budget proposal to Congress. That proposal would cut the National Endowment for the Arts and the National Endowment for the Humanities by 11.7 and 10 percent respectively, and put the Institute of Museum Services out of business.

Hodsoll told the opera group that the president's budget proposal would mean reductions of about 14 percent for endowment programs in theater, dance and other areas. He said he did not expect those cuts to have a dramatic impact on the arts, however. "I think it will have a fairly marginal impact," Hodsoll said privately after the speech. "We've preserved some more money for smaller institutions because they have less access to private-sector money."

In a speech that quoted from the conservative financial weekly The Economist, Hodsoll, a Reagan appointee, sounded the administration theme of increased private support and scaled-down government support for the arts. While recognizing the need for some government aid, he contended that such funds should be used primarily as a catalyst for nongovernment support. "We've got a darned good system -- not a perfect one, but one that compares favorably with any other I know of, and it's working well . . ." Hodsoll told the group.

The Reagan administration has sought cuts in the endowment budgets for the past four years. Each year Congress not only has ignored the cuts but has increased the endowments' budgets. This time, however, congressional arts patrons say, concern over the federal deficit may mean the arts will get less than the traditional largess. The release of the budget is the starting gun in a battle that will go on until April, when Congress appropriates the budget for fiscal year 1986.

Hodsoll's warning notwithstanding, beneficiaries of the arts endowment's grants said they planned no change in lobbying strategy.

"Our credibility is based on the fact that we feel the arts are an integral part of this country. We have an obligation to discuss this with Congress," said Ann Murphy, executive director of the American Arts Alliance, a lobbying group for 350 arts organizations around the country.

"The philosophy does not work," said Robert Herman, general manager of the Greater Miami Opera Association and president of Opera America. "The private sector has been approached by every religious, health and arts organization in America. They can't possibly come close to replacing the federal funds that would be lost."