The Iraqi army, which has been on the losing end of battles with Iranian forces for several months, has begun to give a better account of itself in at least one region of the lingering border war between the two Persian Gulf states.

American analysts are not sure of the significance of this turn of events. But any change in the war, which had largely faded from public attention in the West, is being scrutinized carefully here, in the Persian Gulf and Middle East and undoubtedly in Moscow.

This is because Iran is widely viewed as having turned the tide against Iraq, which started the war in September, 1980, and quickly grabbed a long sliver of land on the Iranian side of the border in oil-rich Khuzestan Province.

The ascendancy of Iran in this struggle is causing concern in many Gulf states that are backing Iraq and fear a resurgence of aggressive Islamic fundamentalism. It is also causing concern here because of increasing Soviet links to Iran.

The recent Iraqi military success came in the border area around the town of Bustan. Late in November, Iranian forces had scored an important success there, driving a wedge between Iraqi units. Early last month, however, the Iraqis launched counterattacks and apparently overran some Iranian positions.

Some senior U.S. specialists do not view these attacks as significant. They say indications are that Iran is engaged in a heavy buildup for what looks like a major offensive that specialists estimate may be forthcoming in the next several weeks.

In this view, the Iraqi attacks around Bustan were mainly probes designed to try to knock the Iranians off balance and disrupt plans for the major assault. These specialists view the Iraqi moves as short-term successes.

The United States does not have formal diplomatic relations with Iraq but the Iraqi interests section in Washington, which has headquarters in the Indian embassy, recently put out a press release claiming that Iranian forces were "dealt a crippling blow" in the early February battle around Bustan.

The Iraqis also claim that widespread reports in the western press about Iran winning the war are incorrect.

Whatever the ultimate impact of the recent Iraqi attacks, the assessment here is still that the war remains a stalemate, but one which threatens the Iraqi government of President Saddam Hussein. The Iraqi ruler started the conflict confident of quick victory but now has his forces stuck in what is widely viewed as a no-win situation.

Despite the lack of formal relations, Hussein has indicated over the past year he seeks better relations with Washington, and Iraqi ties to Moscow seem to be loosening.

Over the weekend, the Reagan administration removed Iraq from a list of nations upon which the most stringent trade restrictions were levied. While this still prohibits military sales to Iraq, the action could give the United States added flexibility to deal with Iraq whatever the outcome of the war.

Sources here say that the Soviet Union has played what they describe as "a cautious, skillful game" in Iran, basically accepting the public insults lodged by the Iranian government of Ayatollah Ruhollah Khomeini in recent years but also continuing offers of assistance.

Even though Moscow has a longstanding friendship and cooperation treaty with Iraq, the Soviets, these sources say, have sold the Iranians some spare parts for armored vehicles and have recently announced a new economic and technical agreement with Tehran.

There is agreement in Washington that the Soviets are making headway encouraging the Tudeh Communist Party in Iran, closely allied to Moscow, to expand its operations and that the Soviets are trying to position themselves to take advantage of the situation when the Khomeini rule ends.

There were rumors last week that the 82-year-old Khomeini was dead but sources here say he is alive, having recovered from what was described as a "period of physical decline."

Despite the more overt involvement of the Soviets in Iran these days, some top administration specialists are skeptical of the ultimate ability of Moscow to have a major influence.

"This is Islamic fundamentalism," one official says. "They want purity."