Leaders of six nations have asked President Reagan and Soviet leader Mikhail Gorbachev, in an appeal made public yesterday, to refrain from further nuclear tests until their next summit meeting and offered to assist in seismic monitoring at test sites to remove doubts about possible cheating.

Its sponsors said the appeal, by present and former leaders of Argentina, Greece, India, Mexico, Sweden and Tanzania, was one of the last political acts of Swedish Prime Minister Olof Palme, who signed it Feb. 28, the day of his assassination.

The declaration, made public in capitals of the leaders and in a news conference here by members of Congress endorsing the appeal, was the group's third presentation calling for nuclear disarmament and a halt to nuclear testing.

In a letter last October, the leaders offered to monitor a comprehensive nuclear test ban by the United States and Soviet Union with seismic devices on their territory and hinted at willingness to undertake on-site inspection on the territory of the two superpowers.

The only U.S. response was a bland three-paragraph State Department statement saying the proposal was under study but giving no encouragement to the ideas, according to Parliamentarians Global Action, which has sponsored the initiative.

Gorbachev, however, sent a formal letter of acknowledgment to the six leaders and met within a few days of the appeal with one of the signers, Indian Prime Minister Rajiv Gandhi. According to the sponsors, Gorbachev said last December that he was willing to accept a role for the six countries in nuclear test verification.

The current appeal makes the six leaders' verification offer more explicit, saying their assistance "could include on-site inspection as well as monitoring activities both on your territories and in our own countries."

These activities, according to the sponsoring parliamentarian group, could include placing seismic stations near nuclear test sites in the United States and Soviet Union.

The Soviet Union has observed a self-imposed moratorium on nuclear weapons testing since last August. That ban runs out at the end of this month but Rep. Thomas J. Downey (D-N.Y.), an official of the parliamentarians' group, said yesterday that there is "reason to think" that the Soviets may extend it until the next U.S.-Soviet summit meeting.

The United States under Reagan has been less interested in banning nuclear tests than previous administrations. A new U.S. test series is expected to begin soon at the Nevada Test Site.

In addition to Palme and Gandhi, other signers of the appeal were President Raul Alfonsin of Argentina, President Miguel de la Madrid of Mexico, Prime Minister Andreas Papandreou of Greece and former president Julius Nyerere of Tanzania.