Sen. Daniel K. Inouye (D-Hawaii), a quiet but forceful member of the Senate inner circle, surprised the Reagan administration and most of his colleagues Monday by breaking with U.S. policy in El Salvador. The reasons behind his potentially influential decision can be summed up in a single word: Vietnam.

For Inouye, who lost his right arm in European combat in World War II, voting for the unsuccessful war in Asia was a painful experience he will never forget. More and more, he sees a parallel in El Salvador, and he is determined not to support a repeat performance.

President Reagan's request for an immediate $60 million in additional military aid to be reallocated from existing programs faces unexpected trouble as a result of Inouye's speech announcing his opposition. The Hawaiian is the ranking minority member and a key figure on the Senate Appropriations subcommittee with authority over the request.

Beyond that, the defection of Inouye marks the highest point so far of political opposition to Salvador policy by the Democratic mainstream in the Senate, and is a likely harbinger of more opposition to come.

Senate Minority Leader Robert C. Byrd (D-W.Va.), who listened intently to Inouye's speech, said that it "will have a considerable impact" on the future course, and quickly announced his agreement with his colleague's viewpoint.

"I agonized over this," said Inouye in an interview yesterday. Addressing his central reason, he said, "One cannot easily forget Vietnam, especially if you had to live through that experience, realizing that your decisions would have affected the lives of many young people."

On Vietnam Inouye had his doubts from the winter of 1965, but kept quiet and kept backing official policy as the U.S. presence rose to 500,000 in 1968. He had been close to President Johnson politically and personally, and broke with the policy only when the My Lai massacre was revealed in 1969, after Johnson was out of the White House.

In El Salvador, said Inouye, he had doubts from the outset, but went along with the policy out of caution and his longstanding inclination to give presidents the benefit of the doubt in foreign policy.

The breaking point came in the past two weeks. On Feb. 28, Reagan called Inouye and other senior lawmakers to the White House to make the case for $60 million in immediate military aid to El Salvador. Nine days later the military aid request was increased by $50 million, to be reallocated from previous requests in a supplemental appropriation bill pending in Congress.

"When the president went from $60 million to $110 million in one week, with no apparent change in the situation, it didn't make sense to me. He also said that if he didn't get the money, we'd increase our advisers [in El Salvador].

"History was repeating itself. I've been conditioned by Vietnam," Inouye said.

Among the other influences on his decision, as Inouye recounted them:

* Secretary of State George P. Shultz' unexpected attack, at a hearing attended by Inouye Feb. 28, on "churchmen who want to see Soviet influence in El Salvador improved."

Last Saturday, in an interview, Shultz suggested that he had misspoke. But Inouye said, "When we start striking at the church, it does not denote strength of our foreign policy."

* Mail from home and advice from about 200 people he has seen on the subject in recent weeks. "The people aren't always wrong. In my mailbag for each letter of support for our involvement in El Salvador, perhaps 25 are in opposition."

This mail is from Hawaii, where the federal establishment, especially the military, was the No. 1 source of income in 1981, and where there are many war veterans. Among his letters were some from fellow veterans of the 442d Infantry Regiment, the Japanese-American unit in which he served in World War II. "These are from men who very seldom write" but now their letters say, "Don't you think one Vietnam is enough?"

* The fact that his son, who is 18, is registered for the draft and thus fair game for a future Salvadoran war. Kenny Inouye is opposed to U.S. involvement in El Salvador but would go if his country called, according to his father.

Similar considerations about policy, its support among constituents and in the family circle were factors in congressional switches about the Vietnam war in the 1960s.

Regarding the future, Inouye said he'd change his view "if I can be convinced that the regime in El Salvador is willing and ready to seek a non-military solution."

Elections in the midst of war are not enough, Inouye said. "We have to face the realities of the situation and sit down with people we despise."

He wondered out loud why the U.S. and Salvadoran governments so resist negotiations with guerrilla forces and their political backers. "After all, the United States sits down with communists all the time," he said.