The Soviet Union announced today that it is indefinitely extending its seven-month-old moratorium on underground nuclear testing beyond the March 31 expiration date and stepped up pressure on the Reagan administration to join in such a ban.

Soviet leader Mikhail Gorbachev pledged that Moscow will not test any nuclear weapons "until the United States carries out its first nuclear explosion." He made the statement in a letter to the leaders of Argentina, Mexico, Greece, India, Tanzania and Sweden that was released by the Soviet news agency Tass today.

Gorbachev first introduced a six-month unilateral ban last August, and extended it on Jan. 15, when he proposed a timetable for worldwide nuclear disarmament. Today's statement marks the first time the Kremlin has made the extension of the ban indefinite and linked it to U.S. testing.

Gorbachev repeatedly has called on the Reagan administration to join the moratorium.

[The Reagan administration brushed aside the new Soviet proposal for halting the nuclear tests, but various officials indicated today that internal discussions are under way about a new U.S. offer on the monitoring of nuclear tests, staff writers Don Oberdorfer and Walter Pincus reported.]

In the past, President Reagan has said that the ban is a long-term goal that has to be seen in the context of "broad, deep and verifiable reductions."

The Soviet Union cannot extend the ban "unilaterally in perpetuity," Gorbachev said in the letter. It has already "paid a certain price," he added, "both militarily and economically."

During summit talks in November in Geneva, the Soviet leader indicated that he had to use a hard-sell approach to persuade some Soviet military leaders to support the ban, according to U.S. officials present during the talks. The latest maneuver by Gorbachev, however, could also be attractive to the Soviet military because it foreshadows an end to the moratorium after the United States makes its next test.

With the new move, the Soviet leader is stepping up pressure on Washington for progress in arms control before it agrees to a date for the U.S.-Soviet summit, in the view of western diplomats in the Soviet capital. He is also strengthening his appeal abroad for support for the ban.

Reagan repeatedly has pressed the Kremlin to fix a date for the summit, but Soviet officials have not responded yet.

Gorbachev indicated in his address to Communist Party delegates here Feb. 25 that his summit goals include progress toward an agreement on the test ban, and on reducing stockpiles of European-based intermediate-range missiles.

"The extra time we granted the American administration is running out," Gorbachev said in the letter to the leaders of the six countries. While Greece is a member of NATO, the others are part of the Nonaligned Movement.

The Soviet leader's letter was a response to a plea from the six, addressed to both Gorbachev and Reagan, not to conduct nuclear explosions.

Gorbachev also indicated willingness to agree to international verification of the ban, which has been offered by the six countries.