A QUIET AND URGENT effort is alive at the United Nations to produce a cease-fire and settlement in the seven-year Iran-Iraq war. The effort rests on maintaining a consistent approach between the Security Council -- especially the two great powers -- and the secretary general. The United States and the Soviet Union are playing, in their ways, the role of enforcer. Javier Perez de Cuellar is the would-be mediator. The striking thing is not the difficulty of their joint task -- that is a given -- but the cautious hope they share that a breakthrough could be near.

The military incident in the Gulf Monday night produced a great swell of anger from Iran's president, Ali Khamenei, at the United Nations yesterday. Yet Iran has received scant international sympathy for its complaint, and Americans seem nervous but generally supportive of this use of the U.S. Navy -- the purpose for which it was sent to the Gulf. A boat of the revolutionary guards had just shot up a British tanker. What American helicopters are reported to have hit was a ship of the regular Iranian navy that had been spotted laying mines in international waters and that was found to have 10 more mines aboard. Interestingly, after his protest President Khamenei picked up the discreet discussions the secretary general has been conducting with Iran to nail down its response to the U.N.'s unanimous peace appeal.

President Reagan, speaking on Tuesday, had challenged President Khamenei to state ''clearly and unequivocally'' whether Iran accepts the U.N. appeal. Iran states nothing clearly and unequivocally. Still, the diplomatic pressures on Iran mount. Iraq gains wider acceptance for its view that a cease-fire confined to sea is unfair and one-sided, and extends attacks by its superior and practically unchallenged air force. Not all Security Council members are as ready as Washington to press on to a second resolution demanding an arms embargo against Iran. But the case for ending the flow of arms to Iran has never been so forcefully made. The huge political risks Iran was earlier willing to take in opening arms-for-hostages dealings with the ''great Satan'' hint at its vulnerability even to a slowing of the flow.

The United Nations resolution offers Iran as well as Iraq great benefit. Of special potential value to Tehran is the unusual provision -- one drafted with its requirements in mind -- creating a commission to examine how the war began. Iraq already says yes. Iran, increasingly isolated, hangs back