The nation paid homage to the courage and sacrifice of its Vietnam veterans yesterday as 120 ex-combat troops and politicians broke ground on the Mall for a $6 million memorial to those who served and died in a war most Americans would rather forget.

"The American people were divided by the war . . . but one point that all Americans can agree upon is that Vietnam veterans deserve recognition and appreciation for their sacrifices," said Jan C. Scruggs, head of the private group building the memorial with congressional approval.

The ceremony, after three years of struggle to create a new national monument without government funds, united Vietnam veterans with traditional veterans organizations, onetime opponents of the war and ordinary citizens. Former infantryman Scruggs and his group received 350,000 contributions from all over the country and defeated a fierce lobbying effort to kill the monument's controversial V-shaped design.

Yesterday in a green and muddy, sun-splashed glade 200 yards northeast of the Lincoln Memorial, the ground breakers, some in military uniforms, stood with shovels along the 500-foot length of the V. The American flag, held by a member of a joint services color guard, flapped behind them in a crisp breeze. "Put your blades to the earth," came the command. "Okay, break ground!" A cheer went up from several thousand spectators. The U.S. Marine Band played "God Bless America."

The names of the 57,692 dead or lost in the war will be chiseled in the order they fell on 10-foot-high black granite walls nestled into a grassy hillock. Inscriptions will honor the 2.7 million who served. In a concession to critics of the original design, there will be a flag and heroic statue of a soldier on the site.

The theme at the groundbreaking was reconciliation, touched with sadness that so great a sacrifice was made in a cause never clear and never won. If there is lingering opposition to the design itself, it didn't mar the ceremony.

"The suffering and the loneliness the veterans bore when they returned home . . . are finally at an end," said Jack W. Flynt, national commander of the American Legion, in his speech. "The frustration and confusion of the American people, long willing but unable to express their gratitude and appreciation to a generation of unselfish patriots, is finally at an end."

Cooper T. Holt, executive director of the Veterans of Foreign Wars, said the memorial will help "create an accord out of our bitterest military experience since the Civil War."

Virginia Gov. Charles S. Robb, a Marine combat officer in Vietnam, remembered the difficulty he had writing families of 23 men who died under his command. "I wasn't able to answer 'why,' and this memorial doesn't attempt to say why, but it does say we cared and we remembered."

"Let this memorial . . . begin the healing process and forever stand as a symbol of national unity," said Scruggs.

Sens. Charles McC. Mathias (R-Md.) and. John Warner (R-Va.), who pushed through a unanimous joint resolution of Congress authorizing the Scruggs group to build a memorial, emphasized the importance and beauty of the two-acre site.

Warner called it "hallowed ground." Mathias, pointing to the sweeping vista to the east where the dome of the Capitol and the Washington Monument are visible through a break in a line of trees touched with a first hint of green, said these are among "the real treasures of America that we spread out in homage to the veterans of Vietnam."

Jimmy Mosconis, Scruggs' former platoon sergeant, flew in from Florida for the ceremony. Mosconis, who once watched Scruggs almost bleed to death when both were wounded in Vietnam, said, "I think it's great. For once since the Vietnam war there'll be something decent come out of it, anyway."

Lew Pullen, a Pentagon lawyer who lost both legs in Vietnam, sat watching the ceremony in his wheelchair. "I'm kind of ambivalent," he said. "There hasn't been any memorial for the Korean or World War II veterans."

Clint Brown, a country singer from Buffalo Gap, Tex., who had a leg and the right side of his skull blown off near Chulai, South Vietnam, said, "I will personally be looking at 27 names of friends on that wall."

Scott Robart, a former psychological warfare officer in Vietnam who flew from New Hampshire for the ceremony, said he was angry that he had to pay $10 for his groundbreaking shovel and wasn't invited to a lunch given later by the Scruggs group. But Robart said, "I love the design. Frankly, I don't like the changes the addition of the flag and statue ."

Vietnam veteran Sterling Doughty, who came from Maine for the ceremony, said he was unhappy that so many big shots and officers were prominent in it, and so few ex-enlisted men. "It's just the same old stuff," he said, referring to life in the military.

The effort to build a memorial began in March, 1979, when Scruggs, of Bowie, saw the movie, "The Deerhunter" and was tormented by flashbacks of his dead war buddies. The memorial idea popped into his head, he said, and he began pursuing it relentlessly, at first with the aid of Mathias.

From the beginning, his idea was not just to honor Vietnam veterans but "also to start the healing process in the country so the country can start recovering from the Vietnam war," he said in an interview.

By April, 1979, he had formed the Vietnam Veterans Memorial Fund, and by July had raised $150. The effort snowballed and Scruggs eventually was joined by 40 full-time volunteers, many of them wives and mothers of men who died in the war. On Jan. 3, 1980, Congress authorized the memorial.

The design was chosen May 6, 1981, in a national competition which drew more than 1,400 entries. The design jury of eight prominent architects and sculptors chose the spare, modern design created by 22-year-old Yale undergraduate Maya Ying Lin.

Lin, a native of Athens, Ohio, whose parents fled mainland China in the late 1940s, designed the monument to blend naturally with the trees and rolling landscape of the Mall. "Walking through this park," she wrote, "the memorial appears as a rift in the earth--a long, polished black stone wall, emerging from and receding into the earth."

While the judges had warned the Fund that the design would be controversial, it wasn't until late last year that opposition became so heated the project nearly was scuttled. Meanwhile, the Fund received the required approval from federal watchdog agencies that Congress had ordered to make sure the design was appropriate.

The approval was warm. Fine Arts Commission Chairman J. Carter Brown said the design had "an extraordinary sense of dignity and nobility . . . because of its great simplicity . . . There is no group of veterans in the history of our country . . . memorialized in such a conspicuous place."

Opposition to the design began in earnest last October, when Tom Carhart, a West Point graduate and twice-wounded infantry platoon leader in Vietnam who now works as a civilian lawyer in the Pentagon, told the Fine Arts Commission that Lin's design was "a black gash of shame and sorrow."

In an emotional statement, Carhart asked: "Are we to honor our dead and our sacrifices to America with a black hole? . . . Can America truly mean that we should feel honored by that black pit? In a city filled with white monuments, this is our reward for faithful service."

Carhart was joined by James Webb, a decorated ex-Marine combat veteran and former counsel to the House Veterans Affairs Committee. Webb called the monument a "wailing wall" for antidraft demonstrators and others, and threw his expertise into organizing opposition on Capitol Hill.

At this point, Scruggs knew he had major problems. The basic Carhart-Webb position was that the monument should be white and above ground, but informal intelligence indicated that the Fine Arts Commission would not accept these changes.

The inscribed names would be harder to read in white stone and the color would make the monument seem bulky. Placing it above ground would add to that problem, would obscure the vistas of trees and other monuments and would detract from the serenity of the Lin design, according to defenders of the design.

Scruggs didn't care. "My personal position was, put it above ground, make it white. I'm here to build a monument, not put a Rembrandt on the Mall."

The opposition gained momentum. The Chicago Tribune called the design "a monumental insult to veterans," and two dozen Republican congressmen wrote President Reagan demanding the design be reconsidered. Sen. Jeremiah Denton (R-Ala.), an ex-prisoner of war in Vietnam, expressed displeasure with the design.

Scruggs was able to draw on strong support for the design by the American Legion, the VFW and other groups. By the time the controversy heated up, hundreds of thousands of Americans and 400 corporations had already sent contributions, most of them since the design had been made public. Many people sent moving letters approving the design.

"The whole idea was to make it the people's memorial, to make it mean something -- not just be built by the government and some corporate money," said Scruggs.

The former U.S. commander in Vietnam, retired Gen. William C. Westmoreland, was a strong supporter of the design, the simplicity of which "strikes me as beautiful," he wrote Carhart.

Nevertheless, opposition grew so intense that Interior Secretary James Watt, one of those Congress named to watch over the design process, withdrew his support for the design and ordered Scruggs to find a compromise with its opponents. In crowded, heated meetings in January and February under the auspices of Warner, the two sides worked out the compromise.

Rushing to break ground as soon as possible so the monument can be dedicated Nov. 11, Veterans Day, the Fund received approval from the Fine Arts Commission and National Capital Planning Commission for adding the flag and statue, with details to be worked out later.

As a result, Watt on March 11 gave Scruggs approval to go ahead with ground breaking.

Neither Carhart nor Webb participated in the ceremony. Carhart, although still not happy with the design or compromise, said in an interview he has given up fighting it.

"I'm not going to be the only one to continue the complaint," he said. "I don't want to be seen as an idle complainer. I can accept a compromise if it's acceptable to everyone else."

Robert Hermann, the American Legion's public relations representative, said the memorial is "an eloquent thing. People have a hard time visualizing it. You have to see the site. It's one of the most beautiful and honored sites in Washington."

As wind swept the site yesterday morning, the ground breakers bowed their heads for the benediction by Army Chaplain Max D. Sullivan. "May this place," he said, "be a holy place of healing."