The Reagan administration has refused to permit the Kremlin's top Americanologist to prolong his current visit to the United States, apparently scuttling a televised Soviet-American debate on the arms race.

The State Department declined to extend the visa of Georgi A. Arbatov, head of Moscow's Institute on the U.S. and Canada, as a protest against Soviet refusal to allow American officials to appear on Soviet television.

According to a senior State Department official, the administration is displeased that numerous Soviet officials have appeared recently on American television while requests for reciprocity in Moscow have been ignored.

Arbatov was one of three Soviets scheduled to debate three Americans next Friday in a special two-hour edition of Bill Moyers' Journal on public teleivision. Soviet sources said yesterday that the other two Soviets would refuse to come if Arbatov is not permitted to take part.

Moyers complained yesterday that the administration is adopting Soviet-style attitudes and "cutting off its nose to spite its face." Different State Department officials have given him different, sometimes conflicting, explanations for the decision, Moyers said.

The first explanation, repeated by a department spokesman yesterday, was that Arbatov had applied for a visa to attend a meeting of physicians on nuclear war, then asked that the visa be extended beyond its expiration Sunday so he could appear in the debate. This switch justified the turndown, the State Department said.

Moyers said that the department had known for weeks that Arbatov was planning to take part in the debate and that department briefers were helping to prepare Sen. Sam Nunn (D-Ga.). one of the American debaters.

Another official, Moyers said, told him "they want to get Arbatov out of the country because his views have been getting so much attention in the press." Moyers said he pointed out that Arbatov would be challenged on the program by three Americans.

A senior department official, Moyers said, had yet another explanation: "We're under pressure from the White House to flex our muscles every time we can" at the Soviets.

Administration officials have noted with some frustration the Soviets' sudden interest recently in appearing on network television.

Two ranking Soviet diplomats have been on Sunday interview shows, and others have appeared on the evening news and other programs. The U.S. Embassy in Moscow has formally suggested that its charge d'affaires appear on Soviet television but to no avail.