THE INTEREST of Yuri Andropov's speech, his first public appearance since taking over from Leonid Brezhnev last month, goes well beyond the part of it on missiles in Europe that has drawn the most attention in the West. The speech indicates that Mr. Andropov landed in the Kremlin leadership running. New American presidents may take up to a year or more to work into foreign policy. Mr. Andropov, long a member of the Brezhnev team, jumped right in. Notwithstanding his early focus on shuffling personnel and bowing to the priority of domestic reform, he plainly intends to take a strong hand in foreign policy, too.

His speech answers some major early questions about the direction he intends to go. The latter-day Brezhnev had sometimes appeared to be bending even more than Soviet Politburo chiefs usually do to the demands of Kremlin arms-builders. Mr. Andropov starts by offering the West a broad program of arms control under the banner of going "back to d,etente." He would negotiate, he says, before undertaking new arms-building; if talks fail, then he will build.

Whether his specific arms control proposals are ultimately negotiable is a necessary and serious question. There can be no doubt, however, that his pitch is carefully designed to appeal to the large constituency in the West, and especially in Europe, that questions Ronald Reagan's policy. Take, for instance, his warning to Europeans that new American missiles "would make peace still more fragile" -- Soviet missiles, of course, make peace more secure.

The Andropov Euromissile position, offering to reduce the number of SS20s to the number of French and British missiles, was immediately rebuffed by Washington, Paris and London. The Western capitals had reason to say no to a proposal that would freeze a Soviet advantage in Europe and force a separation of interest between the United States and its allies. But their rejections will not mean the end of the Andropov proposal. The Soviets must understand, one American official said, that the key lies "in Geneva in serious negotiations and not in trying to influence public opinion." That is very confused and wishful thinking. Obviously Moscow is going to keep on working Western opinion. The alliance is going to have to come up with a better answer to the question about British and French missiles.

In a word, Mr. Andropov, whatever else he may turn out to be, already looks like a formidable adversary. A very difficult time is coming in Atlantic relations. Mr. Andropov is counting on it.