Luxembourg — An increasingly urgent task for President Reagan: trying to kindle public support across Europe for NATO defense strategy against the Soviet Union. Interviews in Amsterdam, The Hague, Antwerp, Brussels, Hamburg, and West Berlin indicate a growing gap between Washington's global perception of the Soviet threat and the more regional, inward-looking, recession-affected views of large numbers of European youth, socialists, churchgoers, and environmentalists.
Significant opposition is growing to the NATO plan to install 572 Pershing II and cruise medium-range missiles to counter the growing arsenal of Soviet SS-20 missiles aimed at targets as far west as London.
Many Europeans see Mr. Reagan working harder to install the missiles than to begin talking with the Soviets about reducing them.
They reject US fears of a growing neutralism in Europe. They say that their countries retain compulsory military service (unlike the United States) and that they kept defense spending high throughout the 1970s while the US was slipping somewhat.
Soviet policy itself is to divide the United States from Western Europe by constantly parading the US as unreliable and self- centered.
One danger of the growing peace movement in Europe is that it could weaken Soviet willingness to negotiate limits to medium-range missiles. it could also weaken the pro- US stand of West Germany's Chancellor Helmut Schmidt -- Washington's key ally in Europe.
A growing peace movement in West Germany itself is lending encouragement to others in the Netherlands, Belgium, and Britain. Even before 120,000 young people staged the biggest antinuclear protest in two decades in Hamburg recently , the German peace movement was laying plans for a new series of demonstrations for this fall.
One well-placed European diplomat, himself pro-American, nonetheless echoed many critics here by remarking to this newspaper:
"Reagan's style is at fault. it should be more sophisticated, more subtle. His simple anti-Sovietism antagonizes all socialists in Europe and a lot of others who want talks to continue.
"It is extraordinary that the Soviets have troops in Afghanistan and threaten Poland, yet [Soviet President Leonid] Brezhnew can project the image that the only problems in the world are caused by the US."
A veteran West European ambassador said:
"Reagan should have fewer spokesmen on foreign affairs. He should go to the Democrats and build a bipartisan foreign policy.
"That way he could reassure us that US foreign policy is and continious and not just based on anti-Soviet slogans."
Europeans want Mr. Reagan to play down the military need for the missiles and to stress their role as a diplomatic tool designed to push the Soviets to the negotiating table.
The December 1979 NATO decision calling for the missiles to be deployed linked that deployment with missile-reduction talks with the Soviet Union. Europeans want Mr. Reagan to emphasize the latter rather than the former, at least in public.
There is a pro-Reagan view in Europe. It argues that the President needs more time to sort out his negotiating positions. It says preliminary contacts have already been made in Washington for a meeting between Secretary of State Alexander M. Haig JR. and Soviet Foreign Minister Andrei Gromyko at the United Nations in September. The State Department has announced that missile talks with Moscow will begin before the end of the year.
According to this pro-Reagan view, the talks will lead to a wider context of SALT III negotiations. Moscow's position is that no decisions reached can be valid until they form part of an ultimate SALT accord.
Some in the pro-Reagan camp, perhaps wishfully, also argue that by concentrating first on domestic economic policies, Mr. Reagan is also helping to make his ultimate foreign policy stronger.
* In the Netherlands, planned placement of 48 missiles there may well have been blocked for many years to come.
Parliamentary sources in The Hague say the elections in May confirmed that the necessary 76 votes to push through approval of the missiles cannot now he obtained. Negotiations to form a new government drag on. Protestant churches lead the most powerful peace movement in Europe. Whatever government coalition emerges is likely to postpone a missile decision when it sends its representatives to the next NATO summit in December.
* In Belgium, government sources say they are confident the 48 missiles to be deployed there will approved, but they cannot answer the crucial question of when. NATO wants them deployed by 1984.
Government sources stick to a deliberately ambiguous government declaration of last December, thus indirectly confirming the strength of the local peace movement.
* In West Germany, the peace movement consists of Protestant youth, socialists, trade unions, and supporters of the "Green" Alternative Movement.
Chancellor Schmidt insists his coalition government will accept its quota of missiles -- but only if at least one continental partner joins him.
It is highly doubtful the Netherlands will join him. Belgium is a question mark. Denmark and Norway agree to the missiles in principle but say they cannot have nuclear weapons on their own soil.
That leaves only Italy. A bright spot for NATO planners is that Italy has agreed to take its share of the NATO missiles and has not changed its position despite protracted talks to hammer out new governments.
* Britain, too, has agreed to take a large share of the missiles. Prime Minister Margaret Thatcher stands firm against a growing British peace movement and against Labour opposition. Her task is made easier because Labour is split into left and far-left wings. A segment of the center-left has departed altogether to form a separate Social Democratic Party.
But NATO planners worry that Mrs. Thatcher could lose the next general election at the end of 1983 if the British economy worsens. Official Labour policy is to give up nuclear weapons.
In the Netherlands, a poll in April showed that a mere 8 percent questioned would accept cruise and Pershing II missiles without reservation. If arms-control talks proceeded simultaneously, the figure rose, but to only 24 percent.
The chairman of the defense committee in the Dutch parliament, Klaus De Vries , spoke for many socialists in Europe when he expressed doubt in an interview that Mr. Reagan was really committed to arms talks. "The new missiles are no real defense," he also argued. "Only four Pershing II sites can actually reach SS-20 bases in the Western USSR. Europe needs to find better answers to the Soviets than missiles like these. . . ."