Last Thursday Kremlin leader Mikhail Gorbachev dispatched a letter to the so-called "Delhi Six" countries in which he announced an extension of the Soviet nuclear test moratorium and simultaneously brought the half-dozen national leaders into the middle of his dispute with the Reagan administration over the testing of nuclear weapons.

Some analysts in the Soviet capital say they consider the letter a deft stroke of superpower diplomacy. Casting the extension of the seven-month-old Soviet moratorium as a concession to a request from the six allows Gorbachev, without leaving the Kremlin, to lobby for his peace proposals and claim support from the leaders of the countries known as the Delhi Six: India, Greece, Tanzania, Argentina, Sweden and Mexico.

"There was an official appeal from the leaders of the six countries," Deputy Foreign Minister Victor Komplektov said in a press conference here Friday. "We have given our reply."

Another potentially important side effect of the international hook-up on this issue between Moscow and these nations is that in the year since Gorbachev came to power and the Delhi Six escalated their campaign for a test ban, bilateral relations between Moscow and all of the six countries have improved.

On Feb. 18, the two-year-old Delhi Six group, which describes itself as committed to improving international security, requested in a letter to President Reagan and Gorbachev that the two leaders ban nuclear testing until the next U.S.-Soviet summit meeting, which is as yet unscheduled.

Gorbachev's compromise response -- extending the Soviet moratorium until the United States conducts a nuclear test -- could be seen in some quarters as strengthening his hand in negotiating a joint ban with Washington by drawing together a camp of proponents outside of the Soviet Bloc, including NATO member Greece, according to western diplomats here.

"Now Gorbachev has an independent lobby for the ban," one western diplomat here said.

But to representatives of the Delhi Six countries in the Soviet capital, Gorbachev's agreement for international verification of the ban in the Thursday letter marks a victory for them.

The six countries offered their services for international verification of a ban on testing in a letter to Gorbachev last fall. "We pushed Moscow on the verification issue," said a senior diplomat from one of the six countries.

In his Jan. 15 arms control proposal, Gorbachev consented to international verification and last week he agreed that the six could assist in it.

Soviet-Indian relations have fared best under the Gorbachev regime. Indian Prime Minister Rajiv Gandhi is the only foreign leader who has held talks with Gorbachev twice in the past year. Gorbachev is due to return Gandhi's visits here with a trip to India later this year and both sides project that trade between the two countries will double in the next five years.

The upswing in Moscow's relations with Buenos Aires since President Raul Alfonsin took office was marked by a successful visit by Argentine Foreign Minister Dante Caputo here in January.

Soviet-Swedish relations have rebounded under Gorbachev. Last week Nikolai Ryzhkov flew to Olof Palme's funeral in Stockholm in his first visit abroad as Soviet prime minister. Next month Palme's successor, Invar Carlsson, is due to visit the Soviet capital.

The Soviet Union is well-positioned to exploit its firmer bilateral ties with various Delhi Six countries to strengthen its hedge against the United States in areas outside of the security field, according to analysts here.

Moscow's closer links to Buenos Aires, for instance, could lead to an increase in its imports of Argentine wheat, at the expense of more costly U.S. grain purchases.

At a time when Washington has ordered the reduction of Soviet personnel in the United States, Mexico City, which already has a large official Soviet presence, is viewed as an alternative for Soviet representation in the region.

As the Kremlin holds out the promise of a "political solution" in the war in Afghanistan, the closer Soviet-Indian relations forged by Gorbachev and Gandhi assure Moscow a counterweight to the U.S.-Pakistani axis in the region.

"We are trying to use the power of the group to bring about an end to nuclear testing," said one Delhi Six diplomat, "and in that sense the Kremlin has been much more responsive to us than the White House."