THE WAR between Iraq and Iran is into its second week and, though each side has no doubt exaggerated the damage inflicted on the other, the toll is substantial in lives and in oil facilities, and the end is not in sight. The parade of tankers that carry oil from other Persian Gulf producers could yet be halted. Iraq's military progress has, moreover, emboldened it to expand its war aims: along with asking Iran's surrender to its several territoral claims and to its demand that Iran stop exporting the Khomeini revolution, Iraq also insists that Iran assure "full democratic rights" -- perhaps a euphemism of the ethnics' autonomy. Iraqi strongman Saddam Hussein seems eager to drive Ayatollah Khomeini from power. To make its point, Iraq is invading a good bit more territory than it claims, evading the United Nations' call for and end to hostilities and resisting all other mediation initiatives.

It is evident that Soviet-armed Iraq is emerging as the dominant power of the Persian Gulf and that, in oil as in geopolitics, it will be more ready to call the shots after the war. This has ignited a quiet debate in Washington between those who, looking at Iraq's power, would have the United States try to accommodate Baghdad and lure it away from its Moscow connection and those who, looking at its radicalism, would have the United States keep a wary distance.At this point hedging seems wiser. "Saddam" has set one bad example by responding to Iran's provocations with what would be called aggression if people were not being so guarded. He has set a second bad example -- one sure to be cited, by the way, to justify Israeli retention of the West Bank -- by seizing territory by force. He has set a third by ripping up an international agreement, the Shatt-al-Arab pact made with Iran only five years ago, in order to press territorial demands.

A week's contemplation has produced few good ideas on how the United States might usefully bring its limited influence to bear. Jimmy Carter floated the idea of an international naval force to ensure transit of the Strait of Hormuz; it was shot down soon after launching by jittery European allies and even more jittery Gulf states. He is now offering to send American air-warning planes to Saudi Arabia. Most of Mr. Carter's regular critics take refugee in the now-unexceptionable suggestion that the United States lacks effective muscle and should develop it. They shy from the harder question of how American force, once restored, will calm the Saddams and Khomeinis of an increasingly willful Third World.

American policy has been more a matter of words than deeds, but the right words have not always been used. "Neutrality," for instance, has dulled the emphasis the United States, an official says all too mildly, "couldn't condone" Iraq if Iraq grabbed the Iranian oil province of Khuzestan. The American interest lies in seeing that the inevitable disputes in the Persian Gulf are settled peaceably. The United States should be losing no occasion to say so.