Soviet authorities refused to let U.S. Ambassador Thomas J. Watson Jr. deliver a traditional Fourth of July national television speech here unless he censored remarks blaming the Soviet Union for the Afghan crisis and deteriorating bilateral realtions.

Watson, in turn, refused the Soviet demands and it is unlikely that the Soviets will back down.

It is the second time in the past three years that the Soviets have barred a U.S. envoy from delivering the Independence Day address, which was to have been videotaped and broadcast tomorrow night on the national news show. t

Watson submitted his remarks to the Soviets several days ago. The speech included the following sentences: "In our view, the recent serious downturn in our relations is a direct result of actions taken by the Soviet side, particularly in Afghanistan. I hope the situation in Afghanistan can be quickly resolved. . ."

U.S. ambassadors have delivered Independence Day speeches on Soviet television since 1974. In 1977, however, Soviet authorities balked and barred then-ambassador Malcolm Toon from delivering remarks that defended human rights.

The State Department has asked the Soviets to reconsider their censorship demand, but embassy sources here said the Soviets have not responded. Moscow has mounted a bitter publicity campaign against Washington, alleging that the United States and China have fomented the Moslem rebellion in Afghanistan in hopes of toppling the Marxist government of Babrak Karmal and installing an anti-Soviet government there.

In recent weeks, the Soviets have gone to great lengths to delete any critical remarks by foreign statesmen about Afghanistan.On Monday, the official Tass news agency omitted West German Chancellor Helmut Schmidt's critical references to the crisis and then took the unprecendented step of rebuking the chancellor during his two-day visit to Moscow for allegedly distorting the truth about the intervention.

Watson intended to express regrets that bilateral relations are strained and to note that he "frequently hears in Moscow the Soviet view that the blame for this belongs to the U.S. The is not the way we see it."

In a related development, Soviet President Leonid Brezhnev omitted any personal greeting to President Carter in his message to the United States noting its observance of the Fourth of July. The note restricted itself to asking the American president to convey to "the American people" the "congratulations of the Soviet people." It did not have the usual expression of personal greeting to Carter.