Moscow — The Soviet Union appears to be escalating its battle with the Reagan administration for the hearts, minds, and parliamentary votes of Western Europe.
While the official press is playing up differences between President Reagan and his European allies, the Soviet Union has formally announced that, at its invitation, West German Foreign Minister Hans-Dietrich Genscher will begin a two-day visit here April 2.
Mr. Genscher is expected to meet Soviet President Leonid Brezhnev, becoming the first senior Western official to do so since Mr. Reagan took office.
Some European sources here are linking the timing of the Genscher visit to an April 6 meeting, not yet officially announced, in Bonn of NATO's nuclear planning group. At this meeting plans to station new US missiles on west European soil are likely to be discussed.
Meanwhile, the Soviet Communist Party newspaper, Pravda, has printed a lengthy detailing of Kremlin arms control proposals clearly aimed principally at a West European aundience.
All Pravda commentaries reflect official thinking. That is what Pravda commentators are paid for . But this article, March 14, was signed by Alexei Petrov -- in the Kremlinological lexicon this is said to be a pseudonym used for authoritative news media messages from the top reaches of Soviet leadership.
The Petrov piece was printed next to news of the planned visit by Mr. Genscher. "It's safe to assume," remarked one Western diplomat, "that the placement was not coincidental."
The main focus of the article, seen here as detailing what the Kremlin considers the most urgent of President Brezhnev's recent suggestions for reviving East-West detente, was on the issue of curbing nuclear missiles in Europe.
Explicitly stressed was Mr. Brezhnev's proposal, made in his Feb. 23 keynote address to the Soviet Communist Party congress, for a mutual freeze on deployment or upgrading of medium-range nuclear missiles.
Both American and European government officials have generally shrugged off the offer as a bid merely to cement a Soviet advantage in that area.
Western sources estimate that the Soviet Union has already deployed about two-thirds of its planned total of some 400 SS-20 missiles -- projectiles, mostly targeted at Western Europe, that are mounted on tracked vehicles. Each missile is capable of hurling several warheads some 3,500 miles.
Plans to station new US missiles in Western Europe, by contrast, are not yet near implementation.
The collective Mr. Petrov said, in efect, that the West Europeans would be much better off forgetting the idea.
The article began with the assumption that NATO members "have not yet decided" on a response to Mr. Brezhnev's proposals.
In what seemed something of a sneak preview of what Mr. Genscher will hear at the Kremlin, the Pravda article scolded the West German minister for allegedly linking arms talks to a prior beefing up of NATO strength in Western Europe.
Then came a carrot and a stick.
The carrot: Although not substantively going beyond recent official Soviet statements, the article explicitly stressed Moscow's willingness to discuss "all matters related to the quantity and quality of nuclear weapons already stockpiled in the [European] region" at talks that would begin "immediately" along with the proposed missile freeze.
The stick: Pravda warned that implementation of NATO's decision in principle to base US missiles in Western Europe "will qualitatively affect the Soviet Union's relations with each of the [West European] countries which provide their territory for the deployment of weapons threatening the USSR."
Such statements cannot but be taken seriously in Western Europe, NATO's front line with the Soviet bloc. Countries like West Germany and France, moreover, have a significant commercial stake in at least passably good relations with Moscow.
Then, too, leaders in West Germany and some other European states must deal with potential parliamentary pressure from within ruling coalitions or from oppositions parties.
One good example is the Netherlands, which Mr. Brezhnev mentioned by name in an aside to European "governments and parliaments" in his party congress speech.
The Dutch government is thought to back the idea of stationing US missiles in the country but to be almsot certainly incapable of getting such a decision through i ts parliament.