In what American officials acknowledged as an attempt to counter criticism of the Reagan administration's defense policies by churches in the United States and western Europe, Vice President Bush today emphasized a claim that President Reagan's proposal to eliminate all medium-range nuclear missiles from Europe is "the strong moral position."

After trying to make this point in every speech and news conference in the five western European countries he has visited, Bush met privately with Pope John Paul II today and referred six times in a 30-minute news conference to Reagan's "zero-zero" proposal as the only one in the U.S.-Soviet negotiations in Geneva that is rooted in morality.

Although Bush declined to disclose the topics he and the pope discussed during a 30-minute meeting, Vatican sources said the missile issue was mentioned.

Bush later used the word "morality" in describing the pope's impact on global attitudes.

The NATO alliance has adopted the zero-zero plan, under which all 600 or so Soviet missiles now aimed at western Europe would be dismantled in return for the West's forgoing European deployment, beginning in December, of 572 new missiles.

That potential deployment has been sharply attacked by church groups in West Germany, Britain and the Netherlands, and by some American Catholic bishops in a pastoral letter.

The pope has neither endorsed nor rejected that pastoral letter. And while he supports disarmament, thus far he has spoken of disarmament as being best achieved by negotiations and in a balanced fashion.

All of the Soviet proposals that have been offered would allow Moscow to retain some missiles in return for no western deployment.

So by stressing the morality of the U.S. plan, Bush is hoping to make points with public opinion and offset some of the authority that church opposition carries.

As Bush prepares to go to France Tuesday and London Wednesday, allied and American diplomats who have watched him on this trip say they believe they are witnessing two fascinating and unusual developments.

One is the tentative judgment that they are seeing American policy gradually and subtly shifting.

The other is that Bush, who has been a largely invisible vice president, is in the middle of what could be one of the most sensitive roles any vice president has played in a long time.

The shift that seems under way is that Washington, while continuing to support Reagan's zero-zero plan, is taking more seriously the possibility of an interim step toward that final goal.

This is what European leaders have been telling Bush privately and what they are increasingly suggesting in public. The allied leaders say zero-zero is the best solution but should not be interpreted as an "all-or-nothing" offer.

They have suggested that perhaps an agreement could be worked out in stages based on a balance of forces at lower levels, and that there be no Soviet monopoly on these missiles, such as now exists.

Every speech that Bush has made has been preceded by an official dedication to the zero-option plan, and followed immediately by a line that the United States will consider any serious counterproposals by Moscow.

The judgment that policy may be shifting is only tentative, however; Reagan will make the final decision.

Bush returns Thursday to report on his private discussions with the leaders of West Germany, the Netherlands, Belgium, Italy, France and Britain.

That is when his role becomes crucial. The question is whether he will simply be a reporter of European views or whether he also will present his own recommendations.

Officials close to Bush say he rarely steps beyond official positions developed in joint government deliberations. But, in part because Bush is probably the official with the freshest exposure to the politically explosive missile issue, some sources say they believe he will provide some advice to Reagan.

Bush's role is all the more important because both allied diplomats and American officials based overseas continue to ask visitors from Washington who will be the architect of an arms control agreement if one seems possible.

They expressed these concerns: the U.S. Arms Control and Disarmament Agency is gutted, and it is thought unlikely that its newly nominated director, Kenneth Adelman, will become an important force in the bureaucracy.

It is widely assumed here that Defense Secretary Caspar W. Weinberger and some of his top aides will be obstacles to anything but the toughest kind of agreement.

Secretary of State George P. Shultz is viewed as a pragmatic and moderate high-level intermediary, but his real views are not known, and he is busy with other issues.

Thus Bush, an unlikely figure just two weeks ago, but a man who sees the president regularly, has considerable political experience and has demonstrated his loyalty to Reagan, becomes a potentially important adviser rather than just a carrier pigeon for European views.

Even if the Soviets reject a U.S. initiative other than the zero-zero plan, many allied leaders say it will show American good faith, tone down public opposition and therefore help them deploy the missiles.

Bush, judging from interviews and an assessment of editorial commentary in each of the countries he has visited, has done reasonably well as a spokesman for the western position.

Nevertheless, he is being told by some specialists that, while it helps to counteract Soviet propaganda, public relations alone is not enough.

The deployment later this year is certain to set off demonstrations in western Europe, and the implications for elections in West Germany, Britain and Italy are serious and unpredictable.

If there is no agreement with Moscow and public opinion in Europe stops the missile deployment, some allied and U.S. officials say they think the NATO alliance could unravel. It could look to many Americans as though Europe is less interested in its own defense than the United States is.