Jimmy Carter, his leadership rejected in an awesome and final judgment by the people to whom he had pledged always to stay close, conceded defeat to Ronald Reagan last night and asked the country to unite behind the president-elect.

With the kind of class and grace that was so often missing from desperate reelection campaign, the president pledged his "fullest support" to Reagan and told his own shattered supporters at the Sheraton-Washington hotel:

"I wanted to serve as president because I love this country and I love the people of this country. Finally, I want to say I am disappointed but I have not lost either love."

Only then, as reached the end of an extraordinarily moving and graceful concession speech, did Carter's voice choke slightly and his tightly controlled emotions become apparent.

But by then it was over and he left the stage to clasp the hands of some of the heartbroken supporters who filled the ballroom. Remaining on the stage while the band played were his Cabinet, advisers and the young men who with him had stormed the White House four short years ago. They applauded and smiled and did the best they could on the saddest day of all for the often-troubled Carter presidency.

The president's appearance in the ballroom at 9:51 p.m. climaxed a physically and politically brutal 36 hours for him. He had left Washington on Monday morning for his final campaign blitz, knowing he was in trouble yet believing with his aides that he could still pull it out. But by the early morning hours of yesterday, before the polls had opened, he knew he had lost. Still he may not have known, may not have dreamed, of the dimension of his defeat. And by early last night he knew even that, and so he wanted to do what he had to do without delay.

At 8 last night he called his press secretary, Jody Powell, and said let's get it over with. "Mr. President, I think you better wait a few minutes," Powell replied.

A short while later at the Sheraton-Washington hotel, an anonymous voice boomed over the public address system, telling the thickening crowd that the president was on his way. "We want to give Jimmy Carter a great send-off because we know that four years from now we're going to be saying what a great president he was," the voice said.

And that they did. As the band, in a moment of bittersweet irony, played "Tie a Yellow Ribbon on the Old Oak Tree," an apparent unintentional reminder of the hostages in Iran, the Carter team took its place on the stage, arrayed in front of a huge American flag.

They were all with him there at the end, Powell and Hamilton Jordan, Stuart Eizenstat and Frank Moore, the members of his Cabinet and his election committee, to listen to what must have been the most difficult speech of his life.

"I promised you four years ago never to lie to you, so I can't stand here tonight and say it doesn't hurt," he said with the familiar grin."The people of the United States have made their choice and I of course accept their decision. But I have to admit not with the same enthusiasm I accepted it four years ago."

He praised the political system for giving the people that choice, paid tribute to Vice President Mondale -- "the best vice president in history" -- and promised Reagan "a very fine transition period, the best in history."

Then he told his people that what they had done had not been lost, that their causes and hopes will endure and he asked of them the full measure of their help for his successor "as he undertakes the task of president of the greatest nation on earth."

There were no tears on the stage from the president and his wife, Rosalynn, and none that could be seen from the men and woman arrayed around them. But there were broken hearts in the ballroom and a single, lingering shout of the campaign now passed -- "you kept us at peace."

Carter's day had begun as the nation slept. Air Force One hurtled him across the country in darkness toward his home of Plains where, with the election day dawning on the east coast, he arrived, exhausted and dispirited, yesterday morning.

The president, showing the physical strain of a brutal, final campaign day that took him coast to coast twice in 24 hours, cast his ballot at the Plains High School just after 8 a.m. yesterday.

It was a weary and dejected Carter campaign entourage that reached the president's hometown as the sun was beginning to burn through the morning fog that shrouded the surrounding fields. They knew by then it was all over, had learned that bitter truth for sure a few hours earlier in the lush far corner of the country so remote from the red clay of Georgia.

The news came in a telephone call to Powell from Jordan, the architect of Carter's remarkable 1976 victory and still his chief political adviser. The results had come in from the final sampling of Patrick H. Caddell, the Carter campaign pollster, and they showed Reagan pulling away, turning what had been a deadlock on Saturday into a 10-point lead by Monday.

In the drizzle at the airport in Seattle, Powell informed Greg Schneiders, the campaign aide who traveled constantly with Carter in 1976. "Pat feels it's severe enough that it's gone," the press secretary said.

At this moment, though, Jimmy Carter didn't know of these final poll findings as he pushed himself through the last agonizing hours of the long campaign. He was then inside a hangar at the airport, bathed in the glare of floodlights, delivering a rousing speech to one of the most enthusiastic audiences he encountered the whole year.

But it was all over except for counting and so a short time later, as Air Force One streaked east high above the country, the president, too, was told by Powell of the poll results. He slept on the plane for a while, preparing for the final public rituals of election day.

In Plains yesterday morning, his emotion showed through only once as he spoke to the people of his hometown, explaining to them defensively some of the difficulties he had faced in the course of a flawed and he knew then defeated presidency.

He spoke to the people from the platform of the old Plains train depot, the exact spot where four years ago he had come home in triumph and openly wept tears of joy.

It was a far different scene in Plains yesterday and the only tears that were shed were not of joy. Rosalynn Carter, her face a study of icy self-control, stood at the president's side as he concluded his last speech of the campaign.

"Many people from Plains, from Americus, from Richland, from around this area, have gone all over the nation to speak for me and shake hands with people in other states to tell them that you have confidence in me and that I would not disappoint them if I became president," he said. "I've tried to honor your commitment to those people. In the process, I've tried to honor my commitment . . . "

Suddenly, Carter paused, his chin quivering as he fought to control his emotions, his eyes filling with tears.

". . . to you," he finally said. "God bless you. Thank you. Don't forget to vote, everybody."

Before he reached the emotionally wrenching end to his last campaign speech the president had tried to prepare the people of his tiny hometown as they stood, the townspeople and the high school band from nearby Americus, on the street in front of the depot.

"We've made some difficult decisions," he said. "some of them have not been politically popular.Some of them have been highly publicized. Some of the crises with which I have dealt, you have never known of them, because they didn't develop into something that affected your life or the lives of the people around the world."

He was trying to tell them, in a sad lament, that he believed he had been a good president in extraordinarily difficult times as right to the end he stuck to his basic campaign themes. Whether from exhaustion, or habit, or just a a stubborn refusal to give up the quest and await the inevitable count, he went on, mechanically repeating to the people of his hometown the sentences of his campaign stump speech.

"The Panama Canal treaty was one of the things that I think is a courageous judgment that we've made."

"We are now importing, as you know, two million barrels of oil a day less than we did just a year ago."

"I've appointed more black judges . . . more women judges . . . more judges who speak Spanish than all the presidents combined in 200 years."

"We've kept our nation strong, kept our nation at peace."