President Reagan called for "a renewed commitment to private giving" to support the arts yesterday as he and Mrs. Reagan honored six arts patrons and six artists at a star-studded luncheon for 120 in the White House State Dining Room.

"You represent the very best in our society," Reagan said. Referring to the honored patrons--the Texaco Philanthropic Foundation, author James Michener, Philip Morris Inc., the Cleveland Foundation, Boston fine arts teacher Elma Lewis and the Dayton Hudson Foundation--the president praised "the great American volunteer tradition."

Speaking at the awards ceremony after the lunch, Reagan said, it is "amazing to me at this time of economic hardship and so much economic need, when the resources must be less, that volunteerism is breaking records."

The administration has sought to slash budgets of federal agencies that support the arts and humanities through grants, but at the same time Reagan has set up a celebrity-packed President's Committee on the Arts and Humanities to find ways to increase private giving.

Yesterday's lunch--where most of the committee members were present, including Frank Sinatra, National Symphony Orchestra President Leonard Silverstein, American cultural ambassador at-large Daniel J. Terra, USIA Director Charles Z. Wick, National Endowment for the Arts chairman Francis S.M. Hodsoll, National Gallery of Art Director J. Carter Brown, Kennedy Center Chairman Roger L. Stevens, retiring Smithsonian chief S. Dillon Ripley and others--was the committee's first major public effort to promote private giving to the arts through celebrity example.

Mrs. Reagan is honorary chairman of the committee. Committee members met in a business session yesterday morning and were treated to dinner by Brown the night before at the National Gallery.

"We started from point zero and we've gotten to point 20," said committee cochairman and former Time Inc. chairman Andrew Heiskell. The committee is also seeking changes in the nation's tax laws to encourage private giving to the arts.

The artists honored were opera singer Frederica Von Stade, Nobel Prize-winning poet and novelist Czeslaw Milosz, painter and sculptor Frank Stella, architect Philip Johnson, director and playwright Luis Valdez and violinist-conductor Pinchas Zukerman .

Two of the honorees, interviewed later on the White House lawn, emphasized that they think government also must support the arts.

"I'm glad to see the private sector is being encouraged. It does not absolve the government from its role," said Lewis, founder of the Elma Lewis School of Fine Arts and the National Center of Afro-American Artists in Boston. She sat next to the president at lunch, and in the ceremony the first lady praised Lewis for "training aspiring young black people for careers in dance, opera and theater."

Stella said he thought the president had "stretched" the definition of volunteerism. "The government has to get behind the spirit of volunteerism," he said.

Michener--honored not as an author but as a patron for what Mrs. Reagan called his contributions of "millions of dollars to help younger writers"--said after the lunch that he makes "an exceptionally good living, which I would be ashamed to keep all myself." Michener provides fellowships for students at the University of Iowa Writers' Workshop and also helped found a yearly competition for poets.

The Texaco Foundation has sponsored the Metropolitan Opera's Saturday radio broadcasts for 42 years and has pledged $5 million toward the Met's endowment drive. Philip Morris is a supporter of the Corcoran Gallery of Art in Washington and of the current Vatican exhibition at the Metropolitan Museum in New York. The Cleveland Foundation is a local community foundation that has raised $11 million for the performing arts in Cleveland in the past several years. The Dayton Hudson Foundation of Minneapolis is a private foundation that supports the arts across the country.

Not every member of the president's committee wants to cut federal support for the arts. Susan L. Davis, a New York public relations consultant who said Reagan appointed her on the recommendation of House Speaker Thomas P. (Tip) O'Neill Jr. (D-Mass.), a family friend, said that if the government would give up a Trident submarine it could use that money to support the arts.

"I don't want the whole flotilla," she said. "I just want one."