Indian Prime Minister Indira Gandhi was back at the White House last night for the first time in more than a decade. Ending that period of sometimes discordant diplomacy between their countries, she and her host, President Reagan, seemed to be singing the same tune of "better understanding."

"My devout hope is that, during this visit, we can weave together all these threads of common interest into a new and better understanding between our two countries," Reagan said in his after-dinner toast to the Indian leader.

"Although our countries may travel different paths from time to time," the president said, "our destination emains the same."

Gandhi responded: "We have had discussions which have been important and useful to us and which I think have created a better understanding . . . In a world where crises so swiftly follow one another, it is important to keep in touch and exchange views even if we cannot agree on all points."

The high point of the evening was a concert on the South Lawn after dinner. With the breeze blowing, lanterns glowing, torches burning and a half-moon shining, Gandhi sat between President and Mrs. Reagan as Indian-born conductor Zubin Mehta led the New York Philharmonic Orchestra.

But the harmony was evident earlier, when Reagan offered extravagant praise for Gandhi's family, which he called the "architect" of India "in so many ways." He likened it to the early American Adams family, which he said "came from Massachusetts, not Kashmir, and by coincidence were often referred to as Boston Brahmins."

In a relaxed mood over coffee in the Blue Room, Reagan said, "What this is all about is a line I've used maybe too often. The troubles in the world are caused by people in the world talking about each other, not to each other." He was wearing his favorite horizontal-pleated formal shirt.

Gandhi wore a simple rose-colored silk sari. First Lady Nancy Reagan wore a peach-chiffon, one-shoulder, sari-like gown with a silver border and silver dots. Asked if the dress was an Indian design, she replied: "It's Adolfo. I've had it for a while. I didn't get it just for this."

Actor Chad Everett, who starred in the TV series "Medical Center," sported the evening's most unusual garment--a black shirt that had ruffles running up the front and around the neck.

He said he spent "some time" with Gandhi's father, Jawaharlal Nehru, on a State Department-sponsored theatrical tour to India in 1958.

"He showed me his hedge garden and panda bears," said Everett, a Wayne State University student at the time.

Other guests included author John Updike; Las Vegas entertainer Wayne Newton; former ambassadors to India John Sherman Cooper, Ellsworth Bunker, Robert Goheen and Harry Barnes Jr.; designer Charlotte Ford; corporate executives Charles J. Pilliod of Goodyear, Roger B. Smith of General Motors and Richard Madden of Potlach Corp.; and Indian movie star Sunil Dutt.

When Wayne Newton was asked if he had any connection to India, he said "I'm an American Indian. I guess that's a connection." His wife said the outing was unusual. "In Vegas he rarely socializes," she said, "but tonight he's having the time of his life."

Mingling with the guests was Secretary of State George P. Shultz, making his White House dinner debut in his new post. "I haven't been here in quite a while," he said. "There's a great elegance to it." He called the president's afternoon talks with Gandhi "positive."

Nicholas A. Veliotes, assistant secretary of state for Near Eastern and South Asian affairs, said Gandhi "accomplished her purpose in coming here, which was to improve relations." He said the president and the prime minister had met for an hour earlier in the day and that the meeting was "very cordial."

They were able to carry on their talks at the dinner table, where Gandhi sat on the president's right and her daughter-in-law on his left. At Mrs. Reagan's table, Gandhi's chief adviser, G. Parthasarathi, sat on her right and Gandhi's son Rajiv, a member of Parliament, on her left.

The dinner, served on the Reagan china, included Seafood Neptune, tenderloin of lamb in golden crust and black cherry bombe. There were three specially chosen domestic wines.

The music was handpicked, too. "Only specific movements were chosen so it wouldn't be long and lugubrious," Nathan Stutch, associated principal cellist, said later.

The 60-member orchestra, whose expenses were picked up by Citibank, played selections from Handel, Mozart, Bruch, Gershwin and Beethoven. Asked if the evening was special to him, Mehta said, "Not musically, but because of the friendship between our two countries. I am Indian and I cannot tell you how pleased I am that my prime minister has come to America again."

Mehta ran through the program at an afternoon rehearsal where White House volunteers held umbrellas to protect the 60 musicians from the sun.

"They have Stradivariuses out there," said Social Secretary Muffie Brandon, who combed the White House for umbrellas.

The decision to seat guests and orchestra under the stars was made at noon when the weatherman forecast a clear evening. A tent had been set up in the Rose Garden just in case it rained.

But by last night, temperatures were balmy as the 116 guests began arriving at the Diplomatic Entrance. First through the door was Shultz. And as he arrived at this musical evening, unsuspecting Navy harpists and flutists played "Send in the Clowns."

Also present were Smithsonian Secretary S. Dillon Ripley and publisher and oriental-art collector Arthur M. Sackler. Neither would comment on a report that Sackler had decided to donate his large and important collection of ancient oriental art to the Smithsonian Institution. The White House said earlier in the day that it was a "total coincidence" that the two men were both on the guest list. At evening's end, when the Marine Band played dance music in the foyer, Sackler was dancing with Mrs. Ripley and Ripley with Mrs. Sackler.

Author Updike has never written about nor visited India, but when asked about why he was at the dinner, he stopped, smiled and said, "I was asked; I thought I'd better come."

Updike, after meeting several guests, drifted toward the corner of the Blue Room with his wife Martha. He said, "I'm a Democrat, actually." Guest list for last night's dinner:

Indira Gandhi, prime minister of India

Rajiv Gandhi, M.P., and Mrs. Gandhi

G. Parthasarathi

Dr. P.C. Alexander, principal secretary to the prime minister

K.R. Narayanan & Mrs. Narayanan, ambassador of India to the United States

H.Y. Sharada Prasad, information adviser to the prime minister

Foreign Secretary M. Rasgotra

K. Natwar-Singh, secretary, Ministry of External Affairs

Dr. A.K. Sen Gupta, additional secretary, office of the prime minister

R.K. Dhawan, special assistant to the prime minister

Usha Bhagat, officer on special duty, office of the prime minister

Dr. K.P. Mathur, prime minister's physician

Hans H. Angermueller Sr., executive vice president, Citibank NA, and Katherine Angermueller, New York City

James A. Baker III, chief of staff and assistant to the president, and Susan Baker

Harry G. Barnes Jr., U.S. ambassador to India, and Betsy Barnes

James M. Beggs, administrator of NASA, and Mrs. Beggs

Melvin Bradley, special assistant to the president, and Ruth Bradley

Ellsworth Bunker and Carol Laise, former ambassadors to India and Nepal

John F. Burlingame, vice chairman and chief executive officer, General Electric Co., and Genevieve Burlingame

Vice President George Bush and Barbara Bush

William P. Clark, assistant to the president for national security affairs, and Joan Clark

Rep. Don H. Clausen (R-Calif.) and Ollie Clausen

John Sherman Cooper, former senator and ambassador to India, and Lorraine Cooper

Carolyn Deaver

Dr. Edward Dimock, president, American Institute of Indian Studies, and Mrs. Dimock

Sen. Robert J. Dole (R-Kan.) and Elizabeth Dole, assistant to the president for public liaison

Edward R. Downe Jr., New York City

Sunil Dutt, leading film star in India

Clifford Evans, vice president, RKO General Broadcasting, and Ruth Evans

Chad and Shelby Everett

James Ferguson, chairman and chief executive officer, General Foods Corp., and Esther Ferguson

Charlotte Ford, New York City

Richard and Ann Gallop, New York City

John and Margaret Gnau Jr., Bloomfield Hills, Mich.

Robert Goheen, former ambassador to India, and Margaret Goheen

Rep. John P. Hammerschmidt (R-Ark.) and Ginny Hammerschmidt

Robert L. Hoguet, director, Tucker, Anthony & R.L. Day Inc., and Constance Hoguet, New York City

Robert and Letitia (Baldrige) Hollensteiner, New York City

John R. Hubbard, president emeritus, University of Southern California, and Mrs. Hubbard

John and Jane Hutchins Sr., High Point, N.C.

E. Pendleton James, assistant to the president for presidential personnel

Sen. J. Bennett Johnston (D-La.) and Mary Johnston

Sen. Nancy L. Kassebaum (R-Kan.)

Alan and Marie Loofbourrow, Bloomfield Hills, Mich.

Edward and Cathey Lozick, Highland Heights, Ohio

Clare Boothe Luce, former ambassador to Italy

Richard Madden, chief executive officer, Potlach Corp., and Joan Madden

M. Peter McPherson, administrator, Agency for International Development, and Mrs. McPherson

Zubin Mehta, conductor and music director, New York Philharmonic Orchestra, and Nancy Mehta

B.K. Mishra, Editor, Hindustan

Mr. & Mrs. C.S. Harding Mott and Isabel Mott, Flint, Mich.

David and Gabriele Murdock, Los Angeles

Donald E. and Susan Newhouse

Wayne Newton, entertainer, and Mrs. Newton

Robert B. Oxnam, president, The Asia Society, and Mrs. Oxnam

Sen. Charles H. Percy (R-Ill.) and Loraine Percy

Charles J. Pilliod Jr., chairman and chief executive officer, Goodyear Tire & Rubber Co., and Betty Pilliod

Secretary of the Treasury Donald T. Regan and Ann Regan

S. Dillon Ripley, secretary, Smithsonian Institution, and Mrs. Ripley

Selwa Roosevelt, chief of protocol, and Archibald B. Roosevelt Jr.

Dr. Arthur M. Sackler, publisher, International Medical Tribune Newspapers, and Mrs. Sackler

Vipin and Padma Sahgal, Los Angeles

Secretary of State George P. Shultz and Helena Shultz

Roger B. Smith, chairman and chief executive officer, General Motors Corp., and Barbara Smith

John F. Sytsma, president, Brotherhood of Locomotive Engineers, and Phyllis Sytsma

John and Martha Updike

Nicholas A. Veliotes, assistant secretary of state for Near Eastern and South Asian affairs, and Patricia Veliotes

Gen. John W. Vessey Jr., USA, chairman, Joint Chiefs of Staff

Rep. Larry Winn Jr. (R-Kan.) and Joan Winn

Secretary of Defense Caspar W. Weinberger