In a one-room basement apartment of the U.S. Embassy now sardonically known as "the Mind-szenty Suite" live 10 Soviet citizens whose stubborn insistence on emigrating to America has brought their lives to a dead end and caused another of the impasses that have characterized Soviet-American relations for more than a year.

The Soviets, seven of whom have been living at the embassy since early summer, refuse to leave without the emigration permission that Soviet authorities have repeatedly denied to them for more than a decade. The Americans cannot get the Soviets to give assurances that there will be no reprisals against the 10 if they leave the embassy compound.

The diplomats and consular officers are not eager to forcibly dislodge the "Embassy 10" because in the past persons who took temporary refuge in the Embassy have been sentenced to prison.

The situation has its roots in Soviet emigration policies. This country makes it very difficult for its citizens to leave. The protracted stay of the 10 Soviets and their adamant refusal to leave has generated new strains for the Americans after the tensions of the spring and summer brought on by the trials of dissidents and the roughing up of several diplomats by the police who keep 24-hour watch at all embassy entrances.

It all began June 27, when seven Siberian fundamentalist Christians rushed past the guards and burst into the shabby embassy consular offices on Tchaikovskovo Street, not far from Red Square.

The Siberian Pentecostalists, consisting of members of two mining families from the Siberian cty of Chernogorsk, about 2,000 miles east of Moscow, are led by Pyotr Vaschenko, 52, the head of a family that includes 13 children. His determination to get to America, where he is sure he can practice his faith without fear of government interference, has brought him to the embassy seven times in the past 14 years. Each long journey has ended in failure - and added to his present conviction that he must not leave until he has a plane ticket to the United States in his hand.

A leathery, moustachioed man who speaks a rural Russian dialect laced with frequent biblical references. Vaschenko has rebuffed repeated embassy attempts to persuade him to leave.

"This is our last hope," he said during a recent interview. "I don't know what they will do to us if we leave, but it will be very bad . . . We are going to leave."

He and his wife, Augusta, 49, and three of their children, Lydia, 27; Lyubov, 25, and Lilya, 21, camped out in the embassy's cultural section for the first two months of their stay. They were accompanied by a neighbor from Chernogorsk, Maria Chmykalova, 56, and her son, Timofei, 16.

At first, the group spent the days sitting on three yellow couches, leafing through English-language magazines and papers they could not read while other Soviets, those with permission to travel to the United States on various exchange programs, or as members of official missions, milled about getting their visas signed.

The seven dined once a day on food donated by embassy staff members. They slept on the couches, huddled under thin blankets, and each took one shower a week in the bathroom of the apartment they now occupy.

They were joined Aug. 11 by three more persons who managed to get by the guards, Eliza Ovsepyan and her two sons, 9 and 5.

Other Vaschenko children are being cared for by relatives in Siberia.

After the Ovsepyans arrived, the Americans redoubled their efforts to get the group to leave. They argued that the "believers", as Christians are generally called here, were hurting their own cause and gaining nothing for other Pentecostalists. But the Siberians remained adamant. It was then that the embassy decided to move all 10 into the basement apartment, which had been used as temporary quarters for diplomatic couriers and others in Moscow temporarily.

Meanwhile, Vaschenko sent a letter to President Carter via two American students who were returning to the United States after studies here. The letter protested that the Americans were trying to force him to leave.

The contents of the letter were made public this week in Washington.

The refugees have a bedroom, a hall, bath, shower, stove and refrigerator. They are able to cook their own meals for the first time in almost three months. There is no radio or television and the youngest children sleep on the two beds while the adults sleep on the floor. The families spend their time reading and praying. The children have toys and games.

The apartment has become known as "the Mindszenty Suite" after the late Josef Cardinal Mindszenty, the Hungarian Catholic leader who spent 15 years living in the U.S. Embassy in Budapest after the 1956 Hungarian revolution.

"Now we can pray whenever we want without hindering other people's work," Vaschenko told reporters recently, giving no sign he intends to leave in the foreseeable future.

"I think they may still be here when I come back for a second tour," said one diplomat.

Fueling Vaschenko's determination is his story of repression in Chernogorsk at the hands of authorities who, he said, began harassing Pentecostalists in the early 1960s. In 1962, he said, officials removed three children from the home on grounds the parents were incompetent to raise them because they insisted on teaching them Pentecostalist doctrine. It is illegal in the Soviet Union to teach religion to those under 18.

Vaschenko and other family members came to the embassy in early 1963, got past the guards and spent several hours asking the Americans to give them exit visas - something the U.S. officials are powerless to do. When they left, some were imprisoned.

Vaschenko made a second journey to Moscow in 1968 and again got inside, agreeing to leave, he said after receiving what he described as an official invitation to emigrate from an American diplomat. Vaschenko was arrested when he left and spent more than a year in Moscow psychiatric hospital, followed by a year in a labor camp.

The Vaschenkos returned to the embassy in 1975, once again gained entrance and again finally were persuaded to leave.

This time, Vaschenko vows, they will not leave until they are certain that the destination will be America.

"God is not far from each of us," he said. "Revelations 17 confirms us in the belief in God and it is our duty to fulfill what God says . . . It is not possible to live this way in the Soviet Union."