A House subcommittee recommended yesterday that the financially troubled National Symphony Orchestra receive a $1 million grant in recognition of its special role as the "resident orchestra of the Kennedy Center."

"I couldn't be more delighted," said Leonard Silverstein, president of the symphony. He said the action shows the orchestra's "critical importance to the nation's capital as a symbol of its cultural significance."

The orchestra, a private organization, has long had money problems. It started its September to May season with a $5.2 million budgeted deficit and is still about $2 million short. In 1981 the federal government had to bail it out with another $1 million grant.

Also yesterday the House Appropriations subcommittee on the interior recommended appropriation of:

* $15 million in grants and loans to Wolf Trap Farm Park, which would give the performing arts center in Vienna the full amount needed to rebuild the Filene Center -- Wolf Trap's main auditorium -- which burned last April.

* $143,875,000 for the National Endowment for the Arts and $130,560,000 for the National Endowment for the Humanities -- the government channels for subsidizing the arts and humanities -- for fiscal 1983. The figures are 43 percent and 36 percent higher, respectively, than the amounts requested by President Reagan.

* $10.8 million for fiscal 1983 for the Institute of Museum Services, a federal office that gives grants to museums around the country and that the administration didn't want funded at all.

Rep. Sidney Yates (D-Ill.), chairman of the subcommittee, said he thinks yesterday's action will be approved by the full committee and by the House and Senate.

"The Congress over the years has been very supportive of the arts , both Republicans and Democrats," Yates said. He said funding for the endowments has "become a nonpartisan program and I feel quite certain the action of the subcommittee will be sanctioned."

National Endowment for the Humanities Chairman William Bennett testified before Yates' subcommittee last April that he strongly endorsed Reagan's $96 million budget request for NEH and refused to say what he would do with more funds if they were appropriated.

Yesterday, after $34,560,000 more than Reagan's budget request had been appropriated, Bennett said, "What the president signs off on, we will spend responsibly . . . You can be sure that if we can't spend it responsibly, we won't." Yesterday's subcommittee recommendation was for the same amount NEH received last year.

The recommendation for NEA was $43 million more than the president's request. The chairman of the arts endowment, Frank Hodsoll, could not be reached for comment.

Carol V. Harford, president of the Wolf Trap Foundation for the Performing Arts, said she was happy with yesterday's action but that -- even if all the anticipated funds are forthcoming soon from the federal government--it is not certain the Filene Center can be open by next summer. The completion date, she said, will also depend on how fast the contractors can work. "We want it by next summer . . . but it might not be possible," Harford said.

Some $2 million in federal funds have already been appropriated by Congress for Wolf Trap. The total anticipated funding is $17 million, $8 million of which must be repaid to the federal government. Wolf Trap has already raised $600,000 toward that repayment, plus another $1 million that will go into the $18 million rebuilding project, Harford said.