In the Middle East's ever-shifting network of alliances and antagonisms, every little movement has a meaning beyond its immediate significance. So it is with today's ceremony at the White House marking the restoration, after a 17-year lapse, of full diplomatic relations between the United States and Iraq.

Administration officials have good reason to play it cool. Iraq is rated by Israel as public enemy No. 1 -- the Arab neighbor that has most fiercely refused acceptance of Israel's right to exist. This week's U.S.-Iraqi diplomatic rapprochement will not sit well with Israel or its supporters in the United States.

With Iraq and Iran caught up in a bloody, costly, four-year-old war, the administration also does not want to prejudice future relations with Iran by playing up a "tilt" to Iraq. For its part, Irq wants no suggestion of a shift that might damage its vital connection with its main arms supplier, the Soviets.

So it looks, for the short haul, like no big deal. But the short view in the Middle East can get in the way of a clear view of deeper meanings. Iraq's choice of this moment to mend the break of the 1967 Six Day War reflects trends that could lead to an important realignment of forces in the Arab world.

To see why this is so, you first have to understand why "normalization" of U.S.-Iraqi relations is happening now. Egypt, for example, restored full relations in 1973 after its 1967 break; Syria did so in 1974. Leaving aside a long stretch when Iraq was consumed with internal political upheavals and a high state of tension with Iran that led to war in 1981, Iraq has been reluctant until recently to pick up a standing American offer for one reason: only a year ago, it looked like a loser in its struggle with Iran. To have reached out to Washington would have been read as a sign of weakness.

The United States, on the other hand, while entertaining no particular sympathy for Iraq's side of the conflict with Iran, desperately did not want Iran to win. In an interview with foreign correspondents in June, President Reagan sent a signal of sympathy for Iraq. He drew a clear distinction between Iraq's attacks on Iranian oil installations (a "fair target" in war) and Iran's indiscriminate attacks on Persian Gulf shipping. In October, Iraqi President Saddam Hussein picked up publicly on Reagan's signal. He said Iraq was reexamining the question of U.S. relations. The reason he gave was that Iraq was now ''strong and capable of protecting itself and serving as a strong shield for its Arab brothers."

You don't have to read too deeply between the lines to recognize a developing sense of common purpose between the United States and Iraq -- and between Iraq, the Persian Gulf oil producers, Egypt and Jordan. All fear the Islamic fundamentalism that drives the Iranian government of the Ayatollah Khomeini; all breathe more easily now that Iraq, while not in a position to win or even end its war with Iran, is a lot less likely to lose it than it seemed to be a year ago.

Implicit, then, in the restoration of relations between Iraq and the United States is Iraq's renewed confidence to hold its own militarily against Iran. Also implied is increased recognition by the Reagan administration that the Soviet Union is not the only threat to U.S. interests in the region. American diplomacy must increasingly bend to the objective of shielding the Persian Gulf and more moderate Arab regimes from Khomeini and the fundamentalists.

Normalizing U.S.-Iraqi relations, Arab specialists argue, also plays into a creeping moderation that may lead to a developing Iraq-Jordan-Egypt axis, with Saudi Arabia a cautious, silent partner. This would leave Syria the angry, vengeful odd man out. So moderation and conciliation are likely to have their usual price: polarization, and violent inter-Arab strife.

But creeping moderation creates diplomatic opportunities, as well. Jordan has broken ranks by restoring relations with Egypt. The Iraqis are said to be ready to press the rest of the Arab states to end the isolation imposed on Egypt for its unilateral Camp David initiative and its peace treaty with Israel -- ready, even, to act on their own, if the others won't go along. At the end of this road lies hope for revival of the stalled Arab-Israeli ''peace process."

What all this suggests is that the United States is not dead in the water in the Middle East, however severe its loss of face in Lebanon. The restoration of relations with Iraq is of a piece with other movement offering new opportunities for the careful exercise of U.S. diplomacy.