Secretary of State George P. Shultz today ended two days of official talks here that centered on control of Soviet nuclear weaponry within range of the Japanese islands.

Arms control issues, especially the question of Soviet SS20 mobile missiles, had been designed by Japan as the main item for the Shultz talks, according to Japanese press reports.

U.S. officials said the subject turned out to have a central place in most of the private discussions.

Top Japanese leaders usually had been uninterested or unwilling to discuss such questions in previous bilateral talks. Why and how the government of Prime Minister Yasuhiro Nakasone was seized with the issue was not entirely clear, but several explanations were being advanced.

First, there is Nakasone's strong personal interest in military matters. A former director of the Japanese Defense Agency, Nakasone created a public controversy by recent bold remarks in Washington advocating a policy of bottling up the Soviet fleet and Backfire bombers in this area through greater military efforts.

Second, a recent commentary by the Soviet news agency Tass threatening retaliation against any Japanese military buildup brought much greater public and official attention to military issues, especially the Soviets' buildup.

Third, the international discussion of arms control negotiations in Europe has spurred Japanese interest in the subject. Japanese officials are taking the view that their country has an important interest in the Euromissiles talks and are making their views felt.

In a news conference today, Shultz again backed the "zero option" calling for removal of all SS20 medium-range missiles in Europe and Asia in exchange for cancellation of U.S. plans to deploy Pershing II and cruise missiles in western Europe.

But he refused to state flatly that the United States would never agree to allow any Soviet missiles to remain in Asia as part of an arms control agreement.