MOSCOW -- "Henry, you are trying to shut us out of the Middle East," Andrei Gromyko said to Henry Kissinger as the short-lived Geneva peace conference of December 1973 convened.

"Well, Andrei, there will now be a hiatus," Kissinger responded with uncharacteristic understatement. He and Egypt's Anwar Sadat then set about accomplishing the exclusion that Gromyko accurately feared.

The hiatus, which lasted nearly 14 years, is now ending as the Russians are forging their way into the Middle East in a big way. Mikhail Gorbachev's diplomatic operatives have made the Middle East the focal point of the "New Thinking" that Gorbachev has demanded in Soviet foreign policy.

Fluidity and tactical adroitness have become the hallmarks of the New Thinking diplomatic style as the Soviets move away from the stolid master designs and stifling ideological commitments of the Gromyko era. Instead of concentrating their efforts on "fraternal" but marginal forces, they focus on each region's most important countries and actively compete to influence them.

While glasnost and "restructuring" remain vague concepts that have not yet succeeded in fundamentally altering Soviet domestic priorities, New Thinking is winning Gorbachev praise and support in Moscow and helping him consolidate his rule.

In the Middle East, New Thinking has involved sending consular officials to Israel as a tiny step toward resuming diplomatic relations, coordinating oil production levels with Saudi Arabia, writing off Egypt's military debt at a time when that issue is a major irritant between Cairo and Washington, and chartering Soviet tankers to Kuwait while Washington hesitates.

Syria, Libya and the PLO, formerly privileged clients, are more likely to be objects of Soviet pressure than Soviet largesse today. Gorbachev's Middle East experts hope to crown their efforts by getting Syria and the Palestinians to attend and cooperate in an Arab summit meeting that King Fahd hopes to host in Saudi Arabia this year.

This seductive theme of new Soviet pragmatism is playing elsewhere in the Third World. In Asia, Soviet overtures to the economically powerful member states of ASEAN and to Japan reassure a Soviet populace weary of tossing rubles into the bottomless pit of Vietnam. In Latin America, Mexico is more important in Soviet calculations right now than Cuba or Nicaragua.

Washington is responding to the new challenge it perceives in all this with what looks suspiciously like old thinking. In the Persian Gulf, Soviet political gains are met with a loudly trumpeted but unconvincing U.S. military response, and a return to Kissingerian language about excluding the Russians from the region.

The idea of a ceremonial Middle East peace conference that would open the way for active American mediation has also been revived by Washington. There seems to be an assumption there that the Russians will once again settle for the appearance of diplomatic parity with the United States and stand aside at a moment decided by Washington.

That is almost certainly not the case. Gorbachev is apparently free of the complexes about parity with the United States that his predecessors possessed, and will hold out for a conference in which the Soviets will have a substantive role.

In 1973, Sadat had already pushed the Russians to the side of Middle East diplomacy. Kissinger could afford to let them a tiny way back in at the Geneva conference, and then excise them again. When he talked of excluding the Russians, Kissinger had specific steps in mind to achieve his goal.

The Reagan administration does not. The Soviets have patiently built up a position in the Middle East and the gulf that no longer depends on U.S. tolerance. More active in both Iran and Iraq than Washington can be, emphasizing common interest with conservative Arab states and Israel, Moscow has created a Soviet role that Americans must come to terms with.

The Soviets are demonstrating that they have absorbed the lessons of Kissinger's successful Middle East diplomacy of the 1970s better than his successors in Washington. While Kissinger is denied a policy-making role in a Republican administration, the man who observed him so closely as Soviet ambassador to Washington, Anatoliy Dobrynin, today sits at Gorbachev's right hand, fashioning a skillful Soviet Kissingerian policy.

As the amateur diplomacy of the Iran-contra affair has proved, such discontinuity is a flaw in the American system that the Soviets not only recognize but have learned to exploit. We pay mightily for our amateurism.