Iran's stop-and-search of an American merchant vessel in the international waters of the Persian Gulf catches the United States in an awkward place. There's an obvious American interest in protecting the American flag on the high seas. At the same time, the Reagan administration evidently wants to preserve a wide latitude to conduct searches itself. To combat the drug traffic, the United States regularly intercepts private ships in the Caribbean. It is not beyond conceiving that it may want to stop shipping going in and out of Nicaragua or Libya.

This may help explain the otherwise restrained, even mild, official response to the Sunday search. The administration stifled protest and granted that Iran as a belligerent had "certain rights" to check neutral shipping for military cargo. But although the ship that Iran stopped was in a war zone, it was not bound for Iraq; it was carrying general civilian cargo from Pakistan to a country, the United Arab Emirates, that is not a belligerent in the Iran-Iraq war. The United States declares itself neutral in that war, although it does not conceal its hope that Iran will accept Iraq's bid to negotiate and its diplomacy is pointed toward that still-elusive end.

In the Gulf incident, the administration took a conspicuous after-the-fact step -- moving up two Navy warships -- to underline American displeasure with Iran's high-seas frisk of the President Taylor. It is weighing providing an escort to other American merchant vessels. It's worth noting, however, that in recent months the Iranians have stopped the ships of more than half a dozen states in a largely unsuccessful effort to choke off Iraq, which, in its own largely unusuccessful effort, has actually shot up ships heading to and from Iran. The Persian Gulf is a place where, for the duration, the course of the war is likely to have more effect on freedom of the seas than international law.