MOSCOW -- With overwhelming support from Central Asia, Kazakhstan, Byelorussia and much of rural Russia, President Mikhail S. Gorbachev clearly won a majority vote for preservation of the Soviet Union in Sunday's referendum despite substantial opposition in Soviet cities, partial returns showed yesterday.
Officials said the pro-union vote was over 90 percent in four republics of Central Asia, 94 percent in Kazakhstan and 83 percent in Byelorussia. It only squeaked by in Moscow (50.2 percent), Leningrad (54 percent) and the key oil region of Tyumen (53 percent) and fell short in the Ukrainian capital of Kiev (44 percent) and the Urals industrial center of Sverdlovsk (34 percent).
An overall total will not be available until later this week, officials said.
Mr. Gorbachev told visiting German Foreign Minister Hans-Dietrich Genscher the positive result in the first nationwide Soviet referendum would hasten the signing of his proposed Union Treaty and would "help divide powers between the center and the republics," Tass reported.
"They will feel like full-blooded states, and the center will be given the opportunity to more effectively exercise functions of vital importance to all, which will be delegated to it by the republics, including the international role of this great power," he said.
The referendum received unusual praise from former President Richard M. Nixon, who arrived in Moscow yesterday on a private visit. "I think it's significant I'm arriving on the day after the first nationwide referendum in the Soviet Union. These are significant changes," he told Soviet television.
But the popular endorsement of a "renewed federation of equal, sovereign republics" promised no solution to the urgent problems Mr. Gorbachev faces. Among them:
* A steadily worsening coal miners' strike, which is crippling the metallurgy industry and is taking on increasingly political tone. Miners in the Ukrainian Donbass coal field joined with those in Kuzbass in Siberia yesterday and added to their demands the resignation of the Soviet president.
* The likely political fallout of price increases averaging more than 60 percent on food and consumer goods, the most dramatic price hikes in subsidized state prices since the 1960s. The government said yesterday that citizens will begin receiving extra pay tomorrow to soften the increases, which are set to take effect April 2.
* Competition from Russian leader Boris N. Yeltsin, who may have come out of Sunday's voting in better shape than Mr. Gorbachev. Russian Federation voters gave overwhelming backing in most areas for a directly elected Russian presidency. If Russian legislators respond to the non-binding vote by creating the post, Mr. Yeltsin will be the front-runner.
* Powerful independence movements in a half-dozen republics, which seem not to have been discouraged a whit by the fact that some other republics voted for the union. Estonia, Latvia, Lithuania, Georgia, Armenia and Moldova refused to take part in the referendum, although Moscow loyalists organized a limited vote in each republic. In the Western Ukraine, 83 percent of voters backed a separate question on independence.
Because the poll could not tame separatist sentiment and because it makes no real change in the standoff between Moscow and the republics, many of Mr. Gorbachev's reformist critics blasted the referendum as an empty propaganda exercise.
Viktor L. Sheinis, a Russian legislator and leader of the Democratic Russia bloc, decried the vote as "a very expensive opinion poll" with no real consequences.
He and others expressed concern that Mr. Gorbachev and the Communist Party hard-liners who now surround him would interpret the pro-union vote as backing for their retreat from democratic reforms the last few months.
There is unmistakable evidence that the retreat is continuing. Soviet television dismissed last week three popular journalists from the Television News Service, an iconoclastic competitor for the staid evening news program "Vremya."
The dismissals followed months of clashes over attempts to censor the show.
Television News Service disappeared from the air briefly, returning Sunday and yesterday a shadow of its former self.
Leonid P. Kravchenko, who has wielded the censor's scissors with a vengeance since Mr. Gorbachev made him chief of Soviet TV last year, recently defended his actions in an interview with The Sun by noting that alternative views were still heard on Leningrad and Moscow television.
He apparently intends to put a stop to that now. On Saturday night the scheduled appearance on Moscow television of reformist historian and Gorbachev critic Yuri N. Afanasyev was banned by a deputy of Mr. Kravchenko's.
The partial military occupation of Lithuania, where Soviet troops seized broadcast facilities in January, shows no sign of ending.
Yesterday, Soviet Internal Affairs Ministry troops detained Audrius Butkevicius, head of Lithuania's Department of Territorial Protection, and interrogated him for 12 hours before letting him go.
Soviet officials alleged that Mr. Butkevicius was illegally carrying three pistols in his car when he was stopped. He told reporters at a Vilnius press conference that he had all necessary documents to legally carry the weapons and that the arrest was politically motivated.