It began as a love story, Soviet style. Virginia Hurt Johnson was an American college student in Moscow on a study program. Sergei Petrov was a handsome and free-spirited free-lance photographer. They met at a dinner party, a group of young intellectuals talking about Pushkin and other giants of Russian literature.

"I was mesmerized," recalled Johnson, a 23-year-old law student from Roanoke, Va.

Their romance was cut short six months later at the airport, two days after an assembly-line marriage at the Moscow registrar's office. Johnson remembered that she was in tears, saying goodbye. "Suddenly a big arm grabs my shoulders and this gruff voice says, 'That's enough,' and drags me away," she says. "And that was the last time I saw him."

Now Petrov is starving to death in Moscow, in the last stages of a hunger strike he began 46 days ago to protest the Soviet government's refusal to grant him an exit visa. His case and that of another hunger striker, Yuri Balovlenkov, have attracted international attention in recent days and become the latest irritants in U.S.-Soviet relations. The State Department and several U.S. congressman have lodged protests with the Soviet government, urging that the strikers be allowed to emigrate under the 1975 Helsinki accords, which require that governments aid family reunification.

But the Soviets have dug in their heels. Last Saturday, they called in foreign correspondents to denounce Western interference in Soviet internal affairs and reiterate that the fasters' visas would not be granted "for reasons of state."

Johnson came to Washington on Friday in an attempt to obtain a temporary visa from the Soviet Embassy so she could join her husband. Her request and a similar one by Elena Balovlenkov of Baltimore were granted.

Balovlenkov, 29, left Baltimore Friday night on what she said was a mission to persuade her husband to abandon his protest fast. Yesterday, she was reunited with her husband, 33, in Moscow and he saw their 2-year-old daughter for the first time.

Johnson, who said she wishes that her husband also would end his fast, was to leave here for Moscow late yesterday.

She said that Petrov is a skilled photographer who is popular among American diplomats and correspondents in Moscow. Now, however, her 29-year-old husband is bedridden in the apartment he shares with his mother. Johnson said that, against the urging of his friends, he has refused all food and drink, save water. She added that Petrov, who is six-foot-one and weighed 180 pounds when he began his fast, has lost more than 40 pounds.

For six weeks, Johnson waited helplessly in North Carolina, where she had been working for the summer. She said that she called Petrov nightly, but that his voice grew fainter with each call and he was becoming less and less coherent. An articulate and composed woman, Johnson said that when Petrov began his protest fast, the couple discussed it over the telephone. "I know it's going to be difficult for you, but I just don't want to live here anymore," Petrov told her.

"I love Sergei and I want to be with him," Johnson said in an interview in Washington on Friday. "But I know I can't tell him what to do. I've always trusted his judgment. I don't think it's my place to tell him to subject himself to the life he has there, the repression he has there, the humiliation he has there.

"They just want to teach him a lesson, to break his spirit, to humble him. But he would rather die than play their silly games."

The Soviets' tough stand on the Petrov and Balovlenkov cases is as baffling to U.S. officials as it is painful to the two men's wives. Every year there are from 15 to 20 marriages between Soviet and U.S. citizens and in two-thirds of the cases the exit visas are granted routinely, U.S. officials said. Yet there is no apparent thread that runs through the remaining cases in which problems are encountered.

Eight years ago, for example, Wooford McClellan, a University of Virginia history professor, married Irina Astakhova, a low-level secretary and translator at a Soviet think tank. Astakhova has been applying and reapplying for a visa since 1974, only to be denied on security grounds. She and McClellan write regularly, but haven't seen each other since.

"God, this security stuff is an absolute fabrication," said McClellan, 48, who still waits in Charlottesville. "I think they just pulled a name out of a hat."

So it appears with Petrov. "It's mysterious to us," said one State Department official, referring to the case. "They've been playing hardball. We've talked to them repeatedly through diplomatic channels, the White House has expressed an interest in it. But their question is, 'What's in it for us?' "

One thing appears clear to U.S. officials: Petrov is no security risk. The alleged reason for refusing him an exit visa is that five years ago he worked briefly as a physicist at a research institute. The institute does classified research, but employes are not given access to military secrets for six months and Petrov left after three months. "It sounds pretty flimsy to us," the State Department official said.

When Johnson first arrived in Moscow in August 1980 she was 21, a Russian-language major from Duke University. The dinner party at which she and her future husband met came two weeks later. She said that the tall, blue-eyed Petrov immediately attracted her attention.

"As a rule, men in Russia are pretty chauvinistic," she explained. "You go to a dinner party and men usually sit in the dining room and eat, while the women do all the work. The first thing I noticed about Sergei is that he was the only man who came into the kitchen and helped the women."

They struck up a friendship. Petrov would guide her around Moscow, taking her to museums and cafes. "It was very platonic at first," she said. "I never told him, 'Hey, I think you're really cute.' "

By November, they were in love. "I asked him to marry me," Johnson said. They wore blue jeans to the ceremony. On March 10, two weeks after Johnson flew back to Duke, Petrov first applied for an exit visa and his trouble began.

The normal waiting period for exit visas from the Soviet Union is three months. On August 14, Johnson said, Petrov called OVIR, the visa office, and was told that his application had been denied two months earlier, although nobody had bothered to tell him. He was told to wait for six months and reapply.

In January, Petrov was summoned to OVIR again and told that his second application had been denied -- even though he had yet to file it. He was expelled from the Soviet photographers' union, leaving him without work. On March 10, Petrov wrote to Soviet leader Leonid Brezhnev renouncing his citizenship on the grounds that his rights under the Soviet constitution had been denied. He began his fast on June 2.

"I don't think anybody in this country can begin to understand what life is like in that country, particularly for somebody as proud and intelligent as my husband," Johnson said. "When Sergei and I were together, we used to have a standard joke: There's one question that you can never ask in this country and that question is, 'Why?' "