IRANIAN minesweepers: it sounds like a contradiction in terms. But even though -- by agreement of everyone but Iran -- it is Iranian-laid mines that threaten navigation in the Persian Gulf, Iranian minesweepers are now out there in international waters trying to pick mines up. Operating in units equipped and trained by the United States in the old days, they are the latest recruits to an international flotilla that includes the Americans, Soviets, British and French, with others perhaps to come.

This development goes beyond the factionalism or disarray or division of labor, whatever it is, that allows Iran to engage in mining and sweeping at the same time. Iran is coming to grant that no Gulf country has a greater interest than it does in free navigation. Unlike Iraq, Iran does not yet have pipelines to carry out the oil that finances its part of the Iran-Iraq war. Did Iran neglect this key fact for a while? In attacking the shipping of Iraq's allies, did it ignore that Americans and others might react by helping to keep sea lanes open? That this new naval presence, while inhibiting Iraq from attacks on Iranian shipping, would also put foreign navies into waters that the Iranians insist are theirs alone to control?

To control and to police: Iranian authorities, denying they laid the mines or command the boats that currently endanger Gulf traffic, declare that they can perform whatever naval services are required and that the foreign ships can go home. To advertise their claim, they invited Western reporters aboard one of their minesweepers on duty this week.

The Iranian minesweepers are welcome: they should know just where to look for the mines. It is cheeky of Tehran, however, to expect the very Gulf states it menaces to entrust the protection of their shipping to Ayatollah Khomeini.

A better idea was offered the other day by President Reagan's national security adviser, Frank Carlucci. ''If the danger {to American-flag vessels} recedes,'' he said, ''the escorting {by the U.S. Navy} can stop.'' Iran, though it is strong on issuing general threats, does not acknowledge responsibility for specific shipping attacks, attributing them to an ''invisible hand.'' But if it is serious in urging the American Navy to leave the gulf, it should want to test this commitment by a ranking official stating the simple condition on which the United States would end the naval operations that Iran finds so offensive