Despite all the surface bows to unity and common purpose, U.S. efforts to rally the West behind a concerted, long-range response to Soviet moves in the Persian Gulf region are encountering considerable reticence from America's European allies.

A month after the Soviet invasion of Afghanistan, that's the perception of many Carter administration officials, even though they rarely let a day go by without reassuring the American public that the allies are strongly behind the United States' new, get-tough stance toward the Soviet Union.

These officials concede privately that the support has been limited largely to such symbolic gestures as curbing cultural exchanges with the Soviets or talking publicly about the possibility of boycotting the Moscow Olympic Games.

America's North Atlantic Treaty Organization allies have been much more vague about their willengness to make the substantive policy changes and put up the money to help meet what one senior U.S. official calls "a serious challenge to which a long-term sustained response has to be made."

U.S. officials acknowledge that the United States must assume the main burden of countering the Soviet Union in the Middle East and Southwest Asia, and they say this acknowledgment was inherent in President Carter's State of the Union pledge to consider the Persian Gulf and its oil "a vital American interest" that will be defended by force if necessary.

Similarly, the officials add, the collective silence with which European leaders greeted Carter's words should be viewed as a tacit recognition of the American leadership role. In private, they say, the Europeans have welcomed this assertion of U.S. resolve toward a region whose oil is even more important to Europe than to the United States.

But the same officials stress that U.S. resolve doesn't mean Washington plans to do the job by itself. While the officials agree that NATO, an alliance structured for the defense of Western Europe, can't effectively expand its collective power into the Persian Gulf, they feel that individual NATO members can provide backup help to U.S. efforts in the region.

Some key administration policymakers striving to put the most hopeful face on the situation, contend that this help already is becoming evident. They cite such developments as moves by NATO countries in the European Economic Community to bolster Yugoslavia and Turkey against Soviet pressures by speeding up the opening of EEC trade links with these countries.

But other U.S. officials say privately that efforts to get the Europeans to commit themselves to measures beyond the limited economic and diplomatic steps instituted immediately after the invasion of Afghanistan have been disappointing, and they are known to be arguing privately that Carter should prod the Europeans to do more.

Almost all U.S. officials agree that the problem stems in part from the dizzying pace of recent events in the Persian Gulf. As one puts it: "We've been asking the Europeans to do so many things -- first in regard to Iran and then Afghanistan -- that the sheer effort of getting them sorted out has everyone's head spinning."

An even bigger problem, the officials add, stems from the vested interest that individual West European governments have in their respective ties to Moscow and to the complex process of East-West detente built up throughout the 1970s.

None is especially enthusiastic about returning to the chilly atmosphere of the Cold War. In the case of some European countries, an abrupt change in the status quo could cause severe trade losses, derail long-planned foreign policy initiatives and trigger strong domestic political conflicts.

French President Valery Giscard d'Estaing does not want to lose the "special relationship" France has nurtured with Moscow for years.West German Chancellor Helmut Schmidt heads a country with a big economic stake in trade with the communist bloc and a political constituency with a strong devotion to detente. Italian Prime Minister Francesco Cossiga must worry constantly about guarding his flanks against the powerful Italian Communist Party.

Even Britian and Canada, the two NATO allies most supportive of Carter's stance, are becoming question marks. There are increasing signs that the Birtish are starting to feel too isolated in their roles as Washington's point man within NATO, and uncoming elections in Canada could replace Prime Minister Joe Clark with Pierre Trudeau, who has hinted at a far less hawkish attitude toward Moscow.

These realities, coupled with the fact that NATO is, as State Department spokesman Hodding Carter points out, "an alliance and not a dictatorship," are understood to have caused a division of opinion within the administration about how much pressure Washington can effectively put on its partners.

Some officials are known to believe that the modest steps the Europeans have agreed to take -- trying to strengthen ties with the oil states of the Gulf area, a West German commitment to help Turkey's troubled economy, British help in putting together an aid consortium for Pakistan -- are the best that the United States can hope for now.

According to their view, any further responses by the allies are likely to be determined less by U.S. prodding than by what the Soviets do in the weeks and months ahead.

If Moscow launches a "peace offensive" aimed at calming West European fears about its intentions, these officials believe, the allies probably would start to feel that the pressure is off and would move in the general direction of France, which has shown itself extremely reluctant to let tensions outside of Europe lead it into situations that might result in the burning of its bridges to the Soviets.

But, the officials say, things could go the other way if the Soviets follow up their Afghan adventure with moves toward other countries in the region, such as Iran or Pakistan, or, as one administration source says, "if they do more gratuitiously dumb things" such as banning dissident leader Andrei Sakharov to internal exile.

U.S. officials say the crackdown on Sakharov appears to have chilled West European perceptions of Soviet policy. In this respect, they note that even the French felt complelled to stiffen perceptibly their attitude toward Moscow. The officials add that the Sakharov incident could be the event that will cause many European nations still wavering over the Olympics question to stay away from Moscow this summer.

For the present, the officals add, the Europeans appear too divided and indecisive about how to deal with the Persian Gulf situation for a single incident to push them clearly in one direction or the other.

But, they stress, if events unfold in a way that sees the Soviet leadership continuing to act aggressively toward the Soviet Union's neighbors or its internal dissidents, the United States may well find that Moscow itself has given the Carter administration the leverage to force its allies into a censensus that they have to back Washington to the hilt, whatever the political, economic and military risks.