The Soviet Union lodged a strong protest with the Reagan administration today over a U.S. attempt to prevent the departure of the son of a Soviet diplomat in Washington. The protest came as 16-year-old Andrei Berezhkov and his parents arrived here by plane.

At the same time, a government statement strongly suggested that the Soviet Union may take similar steps against American personnel and their families stationed in Moscow.

The statement said: "The Soviet government insists that an end be put to these unlawful actions and it warns in the most serious way that those who resort to violation of international commitments as regards others should not think that other standards will be applied to them and that they will not experience in full measure consequences of lawlessness they perpetrate."

Berezhkov, son of a first secretary in the Soviet Embassy in Washington, said upon arrival here today that the entire affair was "a misunderstanding."

He said he planned to resume school and study acting. "I want to be a comedy actor," he said. He told reporters he was "not afraid to come back," and would like sometime to return to the United States, "maybe to stay one week or just to visit."

He repeated his denial that he had written letters to President Reagan and The New York Times seeking assistance to remain in the United States. The Times quoted the youth as writing, "I hate my country and its rules and I love your country."

Speaking in English, he said he was glad to be back in Moscow, adding that he wanted to "thank the State Department" for having been "very helpful in the past few days," adding, to laughter, "Tell them thanks for the ride to the airport."

The family was greeted by a dozen or so people with flowers and the youth was allowed by his father to make only a few general comments before they were driven away.

Following the publication of the letter, American authorities sought to prevent the youth's departure from the United States on the ground that they wanted to interview him to determine whether he was trying to defect to the United States.

During that time, according to Tass, FBI agents and U.S. customs officials "detained without any reason" a correspodent in the Washington bureau of Tass, Vyacheslav Kukharenko, and his family at Dulles International Airport.

Tass charged earlier that U.S. officials violated international law by "flagrantly trying to talk Kukharenko's 15-year-old son into staying in the United States rather than returning to the Soviet Union."

Tonight's Soviet protest described U.S. actions toward Soviet citizens as "disgraceful and inhuman" and dismissed U.S. contentions that they were carried out in accordance with U.S. laws and regulations.

"There exists a norm, generally accepted in the civilized world, on unconditional primacy of international commitments of a state over its domestic legislation," the statement said. It said that this is clearly stated in the U.S. Constitution, which it quoted as saying that all international treaties concluded by the United States "shall be the supreme law of the land."

The Constitution says: "This Constitution and the laws of the United States which shall be made in pursuance thereof; and all treaties, made or which shall be made, under the authority of the United States, shall be the supreme law of the land . . . ."

The Soviet government accused the Reagan administration of violating its commitments under the Vienna Convention on Diplomatic Relations. The convention says that members of a diplomatic mission and their families are outside jurisdiction of the state of residence.

"U.S. officials are keen on prattling about human rights and reading lectures to others on this subject. But the true worth of this prattling was vividly revealed in this instance," the statement said, when the U.S. government "violated with utter impudence" a document it had signed.