A powerful congressional subcommittee has approved sharp increases for next year's federal arts funding, setting the stage for another budget battle between Congress and the Reagan administration.

The recommended levels--$165 million for the National Endowment for the Arts and $150 million for the National Endowment for the Humanities--are 15 percent higher than the current budgets for these agencies and more than 30 percent higher than the administration requested.

House Appropriations interior subcommittee chairman Sidney Yates (D-Ill.) said the action would restore normal funding to the NEA and NEH after two years of administration efforts to bring about "shocking reductions" in their budgets. The agencies support artists, scholars and related organizations with grants.

"It returns funding to the level that had been achieved by every president and supported by every Congress since the creation of the endowments back in 1965," Yates said. "I think it will not be whittled back down" by the House and Senate.

The Yates subcommittee played a key role in increasing the agencies' budgets last year, and its 1984 recommendations are considered key indicators of what Congress will finally approve for next year.

In its action Tuesday, the subcommittee also approved:

* A cut next year in the National Symphony Orchestra's grant--$1 million this year--to $350,000. "Naturally, it's not the greatest development, because the funds are desperately needed," said NSO president Leonard Silverstein.

* A new $350,000 grant to the Washington Opera, which received no direct congressional subsidy this year. "We hope it sets a longstanding precedent," said opera chief Martin Feinstein.

* $350,000 subsidies for the Corcoran Gallery of Art and Folger Shakespeare Library.

* A $21.5 million budget--87 percent higher than this year's budget--for the Insti-tute of Museum Services, the federal agency that aids private museums and that the administration sought to eliminate two years ago. The subcommittee earmarked $3 million of this recommended budget for special conservation grants to 125 American museums to be chosen later.

* $32.4 million for the National Gallery of Art, a slight reduction from last year's $32.9 million, which would hold the museum's federal funds for exhibitions at this year's level. The subcommittee earmarked money for five new art conservators and five new exhibition installers and designers, but at the same time recommended against spending $150,000 to begin summer hours at Easter rather than Memorial Day next year.

* $174.2 million for the Smithsonian, slightly less than the administration request. The committee earmarked $150,000 for developing techniques to conserve museum objects--a program that could be distributed to museums across the country.

$625,000 to subsidize productions at Wolf Trap, the same amount the performing arts center received this year.

* $4.3 million for maintenance of the Kennedy Center--also unchanged.

* $250,000 for NSO concerts at the Capitol on Memorial Day, the Fourth of July, a day in August and Labor Day, plus $250,000 to televise one of the concerts.

Yates said the conservation initiatives at the National Gallery, the Smithsonian and the museum agency represent the subcommittee's longstanding interest in preserving the art and objects of "our cultural heritage."

The subcommittee also recommended that federal funds be used to support either the President's Committee on the Arts and Humanities or the NEA's office of private partnership, but not both. Both of these organizations seek to increase private contributions for the arts.

"You've got a duplication going on," said Yates. He said he was not sure which should be funded. The president's committee is funded this year by about $220,000 from the NEA budget, although Yates had earlier sought unsuccessfully to prevent this allocation.The subcommittee also recommended that $5 million of the NEH budget be used to provide $11,000-a-year scholarships for outstanding graduate students in the humanities. Each scholar would receive $7,000 in living expenses and $4,000 for tuition.

NEH chairman William Bennett said of the scholarship plan, "I'm not sure I like it." He said he thought such a program should perhaps be administered by the Department of Education.

During hearings before the Yates subcommittee and elsewhere, Bennett held firm to his assertion that the current NEH budget of $130.1 million is enough to fund all applications to the endowment that are rated excellent. Of the higher budget recommended by the subcommittee for next year, he said, "It's a lot of money."

If his agency receives this much, Bennett said, "we either get more excellent applications or we look again at the possibility of . . . other new ventures for projects . . . Finally, if we cannot spend the money responsibly, we will not spend it. We've already returned $800,000 last year in unexpended administrative funds, so we've done it before."

NEA chairman Francis S.M. Hodsoll could not be reached for comment yesterday, but a spokesman said that if the NEA budget increases, "naturally we'll make good use of it."