The connection between the hostage crisis and the Iran-Iraq war has forced the United States into a high-risk diplomatic game that could see the freeing of the hostages lead to major new trouble for American interests.

At issue is whether the Carter administration's alleged "tilt" toward Iran in an attempt to influence the hostage issue -- whether through hints of supplying Iran with military spare parts or statements by President Carter and other senior administration officials supporting Iran's "territorial integrity" -- will harm U.S. relations with other key countries in the Persian Gulf region and elsewhere.

Among those who have expressed concern about these points is former secretary of state Henry A. Kissinger, who told reporters in a meeting Friday that supporting Iran too openly in the midst of the war would be a serious risk for the United States because it would create the impression that the Iranians have forced this country to grovel before them.

Another criticism directed against the administration's approach centers on the fact that Iraq, as an Arab country, has the support of most other Arab nations, including Jordan, Saudi Arabia and the emirates of the Persian Gulf. The United States has worked hard to cultivate friendships with those states because of their vital oil supplies or their potential importance to the U.S.-sponsored Mideast peace process, and there is concern that this U.S. effort could be frustrated if they perceive American policy as hostile to Iraq.

The administration's public response to this criticism is to contend that, except for the necessary and legitimate American interest in seeking to free the hostages, the United States is adhering to the policy of strict neutrality it proclaimed when the Iraq-Iran war broke out a month ago.

In private, however, U.S. officials concede that the administration is following a course whose practical effects are weighted toward Iran's side in the conflict.That, they say, is partly a result of the hostage situation. But, they add, even when one looks beyond the immediacy of the hostage crisis there is a logic to U.S. actions dictated by what the administration sees as long range American political and military interests in the Persian Gulf and Middle East.

First, these officials contend, whatever the current hostility between Washington and Tehran, it is not in the interest of the United States to see Iran threatened by territorial losses and internal turmoil that could increase its potential as a source of instability in the region.

The officials add that it is not in the U.S. interest for Iraq, one of the most radical Arab states, to emerge as the dominant military and political power of the gulf region and thereby, put itself in position to increase its influence in the area.

While conceding that the United States has to tread warily in dealing with the conflict, the officials argue that, if these two points are valid, American interests require a policy that will work toward ending the war under circumstances that will prevent Iran's further disintegration and also prevent Iraq from reaping the benefits of military agression.

Elaborating on this thesis, the officials point out that Iran's strategic location and its position, under normal circumstances, as the world's second-largest oil exporter make its stability a matter of vital international concern.

After a long period of revolutionary ferment and internal power struggles that came to a head in the hostage crisis, U.S. officials lately have been encouraged that Iran seemed to be moving toward evolution of a new internal order -- one that, while not particularly friendly toward the United States or the West, would at least have the capacity to defuse the country's potential as a tinderbox and restore some semblance of rationality in its dealings with the rest of the world.

Now U.S. officials fear that an Iraqi military victory that would take large chunks of Iranian territory and humiliate Iran's Islamic clergy-dominated government could unleash a new wave of internal unrest marked by new separatist movements among Iran's various minorities and a political backlash against the present leaders.

Under a worst-case scenario, that could mean the kind of internal distegration that would shift power from the rightist factions led by Ayatollah Ruhollah Khomeini to the extreme left. In addition to becoming susceptible to an internal takeover from the left, an Iran weakened in this way would be much more vulnerable to pressure and possible territorial grabs from the neighboring Soviet Union.

That is why Carter, Secretary of State Edmund S. Muskie and other senior administration officials have spoken out in recent days against the "dismemberment" of Iran. Their remarks, administration sources say, were aimed not merely at trying to influence the hostage issue but also at pointing up a situation with potentially dangerous consequences for the West.

Looking at the other side of the equation, U.S. officials find little comfort in Iraq, with its frequently unpredictable radical tendencies and its ties to the Soviet Union, being able to use a victory over Iran as the vehicle for imposing itself as the new power in the Persian Gulf.

If Iraq were to gain that status, it would be able to influence Saudi Arabia and other gulf states to put distance between themselves and the United States on a wide range of crucial issues ranging from cooperation on oil supply and pricing policy to efforts to entice the Arab world into the drive for resolution of the Arab-Israeli conflict.

In seeking to circumscribe Iraq's ability to play such a role, U.S. policymakers are keenly aware that they are walking a tightrope because of the support that has been given Iraq in the name of Arab brotherhood. Jordan's King Hussein, brushing aside U.S. pleas for moderation, has been especially vehement in championing Iraq's cause. Gulf states such as Saudi Arabia, caustiously testing the winds, have openly expressed sympathy for Iraq.

But U.S. officials believe Arab unity is not as solid as it appears. For one thing, the officials note, radical Arab states such as Syria, Libya and Algeria, which are in competition with Iraq for leadership of the Arab world, have either openly or tacitly denounced Iraq's role in the war.

Even more important, U.S. officials think that the gulf states backing Iraq have done so more out of prudence than real affection for the Iraq cause and that what they want most is an end to the fighting before it threatens to involve them.

These are the considerations that led the United States to the proposal signaled by Muskie in a speech last Monday. In broad outline, he called for Iran to stop inciting Iraq's Shiite Moslem population against the country's Sunni Moslem leaders, for Iraq to withdraw at least partly from the Iranian territory taken by its forces and for both sides to submit their territorial dispute to mediation or arbitration.

The U.S. hope is that other countries with a stake in the conflict will pick up the scheme and push it in a forum such as the Islamic Conference inside the United Nations or the U.N. Security Council. The hope is that eventually Iran, because it is unable on its own to expel the Iraqis, and Iraq, through persuasion from other Arab countries, will seize on this plan as a mutually face-saving way of ending the fighting.

A major complication in pursuing this goal is the perception that the United States essentially is siding with Iran and that the U.S. professions of neutrality don't square with the fact that a release of the hostages could compel the United States to free more than $400 million worth of frozen Iranian military equipment in this country -- equipment that Iran theoretically could use on the battlefield.

U.S. officials respond that, while that looks like a breach of neutrality, it isn't. They point out that even if the hostages were released immediately and Carter responded instantly by unfreezing Iranian assets, administrative, logistical and legal problems would mean a considerable time lag before any sizable amounts of the equipment would be in Iranian hands ready for use.

Thus, even if the U.S. military supply pipeline to Iran should be reopened -- an option that the officials say is still very theoretical -- that development would have to be viewed in tandem with the drive to bring about a cease-fire and mediation.

In other words, if a cease-fire could be achieved soon, the fighting would be over before the Iranians had the American equipment. At that point, according to this argument, the infusion of weapons and spare parts into Iran would probably help to buttress the peace: Iran still would not be strong enough to attack Iraq, but it would be reinforced sufficiently to make the Iraqis think twice about invading Iran again.