With his own diplomats expressing alarm about frayed post-war ties with the Arab world, President Bush has asked deputy national security adviser Robert Gates to draft a plan to find U.S.-Arab harmony.

Bush himself made an overdue but major move toward this goal Friday, when he decided to end months of angry exchanges between the United States and Jordan to which he had been a heavy contributor. He called Jordan a "tremendously important country in this new world order," a big change from last August, when he denied it economic help because King Hussein stayed out of the anti-Iraq coalition.

But Jordan cuts a relatively minor figure on the Middle East's post-war chess board. After Saddam Hussein is knocked out, the heavy players will be Egypt and Saudi Arabia, vying to be Uncle Sam's closest ally; Turkey, which is suspected by Syria of eyeing territorial acquisitions in a decimated Iraq; and Iran, the once-and-future colossus of the Persian Gulf. Once the Gulf war ends, Bush and Secretary of State James A. Baker III will push Israel as hard as U.S. political reality permits to resolve the Palestinian dispute. But the Arab-Israeli struggle is old and has stymied every president since 1967.

Gates's study centers on what is new and uncharted as a result of Arab membership in the anti-Saddam coalition: the rise of Saudi Arabia and Egypt and the sudden warming of long-icy relations with Syria, next to Libya the most consistently anti-American state in the region. But just as Hafez Assad renews relations with Washington, he runs into trouble with the Turks.

In Turkey, President Turgut Ozal's unexpected offering to Bush of the Incirlik air base for strikes against Iraq has caused much anguish in Damascus. Syria sees Turkey stirring unrest among Kurdish minorities in Iraq, Turkey and Iran in order to get a piece of Iraq. That is viewed as a security threat by the Syrians, who contend the Turks are willing to pay for U.S. acquiescence to their plans by offering Incirlik.

Bush and Baker showed few signs of coming to grips with these and a host of other postwar issues until the president asked Gates to head a high-level panel of CIA, State Department and National Security staffers. It is none too soon.

"We'll win the war, and then maybe in a year we will begin to understand the meaning of what we have done in destabilizing the old regional balance of power," retired Gen. William Odom, former head of the National Security Agency and deputy national security director for President Jimmy Carter, told us.

Despite his fascination for foreign affairs, Bush's long suit is not strategic planning -- or what one insider calls "conceptual concentration." He loves hands-on management with heavy personal involvement, particularly on the telephone, plus meticulous attention to how his aides and advisers are carrying out his policies.

Almost before Deputy Secretary of State Lawrence Eagleburger had climbed off his plane on returning from Israel last week, a White House source told us, Bush summoned him. He wanted Eagleburger, still in his traveling blue jeans, to deliver a personal briefing on his mission to Jerusalem to talk the Israelis out of retaliating against Iraqi missile strikes. But that attention to detail is not the same as planning postwar chess moves.

On our recent swing through the Middle East, we found alarm among many key diplomats, both American and European, over Bush's failure to lay down even a bare outline for policy in the new Middle East that will emerge when its first U.S.-vs.-Arab war has ended in an expected four to six weeks.

Arab leaders told us that the president of the last remaining superpower frequently dismayed them with his personalized invective against the Iraqi dictator. If that's how the leaders felt, the Arab street has been far more deeply affected by Bush's blunt, often crude, rhetoric.

Coupled with the awesome pounding Iraq has taken from bombs, missiles and other ordnance in America's war machine, Arab masses may resent Saddam's humiliation by Bush even though their admiration for the Iraqi tyrant is not universal. Sympathy for a defeated Saddam plays into the hands of anti-American nationalists and the Moslem fundamentalists who want the United States to get out and stay out of their land.

Preventing rampant anti-Americanism may become the most difficult of Bush's problems, requiring all his political skill. The buildup of mass Arab resentments would quickly wipe out the gains of Bush's masterful performance as commander in chief. This is one conflict where postwar planning must start with the shooting, and the president has finally begun to tackle a task he obviously relishes less than leading the punitive expedition against Baghdad.