Andrei Berezhkov, the 16-year-old Soviet diplomat's son who was at the center of a U.S.-Soviet tug of war for eight dramatic days, flew home last night after telling reporters and two American officials, "I want to go home and not stay here."

The blond, curly-haired youth, wearing blue jeans and Nike sneakers, said he was not under any pressure from the Soviet government and had not written the two letters to the White House and The New York Times that set off the diplomatic standoff. The letter to the newspaper, signed "Andy" Berezhkov, said "I hate my country and it's sic rules and I love your country."

Yesterday, after asserting that he wanted to leave, the boy, speaking in English, said, "I say what I feel and what I want to say."

A seven-minute interview in the immigration lounge in the international departure area at Dulles Airport culminated a week-long standoff between the State Department, which insisted upon interviewing the youth, and the Soviet Embassy, which was equally adamant in asserting that no interview would take place before the youth and his family left the country.

From its inception, the affair swiftly spiraled into an international incident engaging the personal attention of Secretary of State George P. Shultz and President Reagan.

Standing nearby during the airport interview was the No. 2 official in the embassy, Oleg Sokolov, and two assistant secretaries of state, Richard Burt and Elliott Abrams. Neither of the American officials asked any questions.

At 7:08 p.m., about an hour after the interview ended, a red and white TWA jet taxied down the runway and took off for Paris, carrying the boy, his mother, Lera, and his father, Valentin M. Berezhkov, a prominent Soviet diplomat.

Moments later the State Department issued a statement asserting that after hearing the boy "state his wish to return home with his parents in a situation where he could make a choice," Burt and Abrams "made the determination that he was voluntarily departing the U.S."

During the brief airport interview, conducted by three reporters chosen by lot by the State Department, the boy appeared relaxed and occasionally smiled shyly.

As the interview neared an end and the family was being hustled from the lounge by officials, the boy told reporters he wanted to be "an actor . . . in Moscow."

A moment later he turned back toward the reporters, raised his hand and said, "Say hi to Mick Jagger."

With that, the boy walked off with his parents and Soviet officials, leaving unanswered many questions about the episode.

The Soviet contention that any official questioning of young Berezhkov would be a violation of international law was reiterated earlier yesterday when another set of three American reporters, selected by the Soviets, met with the Berezhkovs at the Soviet compound on Tunlaw Road.

The youth's father charged that the United States was attempting "to use our boy as a pawn in a new anti-Soviet gambit."

"We categorically reject any idea of organizing any kind of interview," he said. "We are a diplomatic family; we have diplomatic immunity."

The drama began last Wednesday when the youth disappeared from his family's home, in a Friendship Heights apartment building just across the D.C. line in Montgomery County. The Soviet Embassy reported to the State Department later that day that the youth had disappeared with his family's car, though the family did not believe he knew how to drive. The incident was reported to police, who put out a lookout for the youth. But on Thursday morning Soviet officials notified the State Department that the youth had returned at about 4 a.m. that morning.

The State Department later learned that the New York Times and the White House had received letters, purportedly signed by the Berezhkov youth and making it appear that he wanted to defect to this country.

That day no one answered at the Berezhkov's apartment, and a contingent of FBI and Secret Service agents began to stake out the apartment and the Soviet compound on Tunlaw Road. The agents peered into vehicles departing through the compound's iron gates.

Meanwhile negotiations were going on between the State Department and Soviet officials, but neither side--at least publicly--appeared to move from its position.

State Department officials said they were willing to accept assurances from Soviet officials that the youth and his family were in the Soviet compound. However, no one saw the youth and his exact whereabouts remained a mystery.

Yesterday in the airport interview, the youth said he had been "in the embassy" since last Thursday. He said he had led "a normal life" there and had "watched TV."

Asked why he ran away from home, the youth said, "I didn't run away. I just wanted to drive around the city. That's it. It was evening, and I fell asleep. That's why it took so long."

At one point during the airport intervew the youth's mother broke in to say, "We want to go home. We want to go home very quickly."

The father, an urbane and sophisticated figure on the Washington diplomatic scene who was welcomed into the homes of many professors and journalists, opened the interview session by saying that he would return to the Soviet Union and continue "to work for the benefit of Soviet-U.S. relations . . . to normalize our relations." He said that he had represented the United States and Canada Institute here for five years. The institute is in effect a Soviet think tank on American affairs.

He said his family planned to go home "in the near future, but now it is accelerated a little bit." Then he told his son, "Andrei, I think you can say a few words."

After the youth opened by saying that he wanted to go home, Sokolov interrupted and looked at the two U.S. officials, saying "I register to Mr. Burt that this is the clearly expressed desire of Andrei Berezhkov to return to the Soviet Union with his father and mother."

At another point, Sokolov interjected, "No more questions are necessary." Finally, Sokolov said, "Very good. Thank you, gentlemen and ladies. This is the end of our conversation."

Many relevant questions about the episode remained unanswered when the Berezhkovs departed. From the outset Soviet officials said the letter written to the New York Times, and a second addressed to President Reagan, "appeared to be forgeries."

U.S. officials have not produced the letter sent to the White House, nor have they said what their investigations revealed about the authenticity of the letters. A New York Times spokesman yesterday said that the newspaper had tried without success to verify the authenticity of the letter it received, and "we assumed it was authentic."

A State Department spokesman, in referring to both letters, said yesterday only that "we had no reason to believe they were forgeries."

Valentin Berezhkov repeated yesterday what Soviet officials had been saying all week, that the letter in The Times contained "American cliches" which he maintained his son never would have written. In addition, he said scornfully, "look just at the signature--you would think a 16-year-old boy knows how to spell his name."

In the published letter, the signature appears to have a syllable missing, looking more like "Andy Berzhkov" than Berezhkov.

Another unanswered question was what young Berezhkov did in the time he was absent from his home, driving his father's car with diplomatic plates. The father described the escapade as "a childish thing," with his son absent "for about 10 hours or more."

Valentin Berezhkov attributed the escalation of the affair to "a consequence of our overall bad relations with the U.S."

When asked if his son would be permitted by his parents to remain in this country if he wished to do so, the father said, "Why would he want to stay here? There is no question of staying here--It is quite excluded."