Board members of the foundation that runs Wolf Trap Farm Park began planning last night to rebuild the theater destroyed by fire Sunday night and to go through with as much as possible of the scheduled performing arts season. President Reagan also moved to see what help he could give.

The Wolf Trap board resolved at an emergency meeting here to stage as many as possible of this summer's engagements in available or makeshift facilities "even if it means a massive circus tent" at the nationally known performing arts park, said Board Chairman Robert Keith Gray.

In addition, Gray said the board officially called for the rebuilding of the center and agreed on one proposal to raise money by asking contributors to donate $1,000 to "buy" seats for the public in the new theater. The seats would bear plaques with the donors' names.

Earlier yesterday, Reagan appointed Interior Secretary James Watt and National Endowment for the Arts chairman Frank Hodsoll to assess the damage done by Sunday night's spectacular blaze.

Reagan was one of an array of public officials, ranging from Watt to Fairfax County Board of Supervisors Chairman John F. Herrity, who lamented the destruction of the $5 million open-air Filene Center. White House communications director David Gergen told reporters Reagan telephoned philanthropist Catherine Filene Shouse, who donated the land for the park and $2.3 million to build the theater to the federal government 11 years ago. "It's a tragic thing, and we'll just have to see if we can help," Gergen quoted the president as saying.

As investigators sifted through smoldering rubble, state and federal officials, including Virginia Gov. Charles S. Robb and Rep. Frank R. Wolf toured the 117-acre Fairfax County site and called for the rebuilding of the cedar-paneled, metal frame theater located in the only national park for the performing arts.

Wolf Trap officials were also reportedly discussing with the National Park Service ways to salvage the season that is scheduled to begin June 8 with a gala dinner and operetta performance.

Gray, a prominent Republican who operates a public relations firm here, said the opening events would go ahead at the park as scheduled, possibly in a tent.

He also said that as part of what were described as a large number of calls of encouragement and support from performers and members of the public yesterday, both the Kennedy Center and the National Theater had offered their facilities on nights when they are not being used.

"We're going to talk to anyone with command of big facilities," Gray said.

Investigators said they were baffled by the cause of the blaze, which was not completely extinguished until 3 p.m., nearly 17 hours after it began. "It's far too early for us to make a statement about the cause," said Bob Martin, an investigator with the Virginia State Police.

Fire officials said arson has not been ruled out and arson investigators routinely surveyed the scene. The severity of the fire, which twisted steel beams and melted the aluminum roof of the 6,500-seat amphitheater, prevented investigators from reaching the stage area where the fire is believed to have originated.

The fire was the sixth in the 11-year history of the park, a major cultural center located 15 miles west of Washington near Dulles Airport.

The most serious of the previous fires occurred in 1971, 15 weeks before the opening of the towering theater donated by the 85-year-old Shouse, the daughter of Mr. and Mrs. Lincoln Filene of Boston.

That blaze, which destroyed a major portion of the nearly completed theater, was believed to have been deliberately set, as were two other less serious fires that occurred in 1976 and 1979.

After the 1971 fire, Fairfax County fire officials recommended that the National Park Service install a sprinkler system. Because the park is federally owned, however, Wolf Trap is not required to meet state or county building and fire codes. Park Service officials said yesterday that after that fire, which did an estimated $600,000 damage, Wolf Trap did not have the money to install a sprinkler system.

"It would have helped every time they've had a fire, if you want to know the truth," said Alfred Savia, deputy Fairfax fire chief.

Park Service spokesman Sandra Alley said an automatic sprinkler system located in the stage area, where the fire apparently broke out, was being installed at a cost of $286,000 and as of Sunday night was "95 percent complete," but wasn't yet working.

Fire officials said yesterday that they believe the fire started near two wooden columns at the front edge of the stage. Officials said that the guard on duty, identified as Henry Collier, was in his office located beneath the stage, when he heard what sounded like an explosion. Collier reportedly left his office, saw flames shooting through the roof above the stage, ran back to his office to report the fire and discovered the phone was dead.

Fairfax fire officials said the blaze was reported by a nearby Park Police officer who radioed the Fairfax emergency switchboard at 9:47 p.m. When firefighters arrived five minutes later they found the building engulfed by flames, whipped by 30-mile-per-hour gusts.

Although public officials and Wolf Trap executives vowed to rebuild the theater, the chief unanswered question is who will pay for it. Wolf Trap, like all property owned by the federal government, is "self-insured." That means that the federal government does not pay insurance premiums because it has sufficient financial backing to meet liability claims. In the case of Wolf Trap, officials said there is no money set aside to rebuild it.

Officials from the House Interior Appropriations Subcommittee said they would view with sympathy a request for funds to rebuild the center.

"We will rebuild? Absolutely!" said Wolf Trap spokesman Larisa Wanserski. "But it's got to be the responsibility of government and the private sector. And until the reports of the damage are in and assessed, we won't know who's going to contribute what."

Wolf Trap Board Chairman Gray said last night that contributions could be sent to Wolf Trap Foundation, Washington, D.C. 20260.

"I've been very much moved by the response of everyone," Shouse said last night after the emergency board meeting at her Washington town house.