Sweden's Prime Minister Olof Palme dispatched a formal note this week to NATO and Warsaw Pact governments seeking support for a plan to remove short-range or "battlefield" nuclear weapons from a swath of central Europe, an idea that he says would sharply reduce chances that a smaller conflict might escalate to Armageddon.

Given the host of other disarmament proposals currently on the agenda, Palme's foray is plainly a long shot. But the fact that he is pressing it publicly confirms that the intense, hard-driving Palme, whose Social Democratic Party was returned to power by Swedish voters this fall after six years in opposition, intends to pursue the outspoken international activism that has made him Scandinavia's best-known political leader.

"The sheer irrational madness of the arms race has become ever more obvious to me," Palme, 55, said in an interview at his office. "Why should the superpowers go on piling up nuclear weapons to an ever increasing degree of insecurity? I have become an increasingly firm believer in arms control and real reductions. . .

"The alternative is horror. There is no doubt in my mind that there will be world wars that would lead to the obliteration of mankind." Removing some of the thousands of small nuclear warheads arrayed on both sides of Europe's divide would be, Palme said, a welcome, if limited, "confidence-building measure."

In his years out of office, while another politician might have concentrated on the domestic front, Palme honed a claim to expert views on disarmament and other global matters in a series of high-visibility foreign roles and assignments. The idea of a nuclear-free zone, for instance, was put forth last spring by an "Independent Commission on Disarmament and Security Issues" which Palme chaired and that also included former secretary of state Cyrus Vance and Britain's ex-foreign secretary, David Owen.

Earlier Palme served as a key member of the Brandt Commission, under the chairmanship of former West German chancellor Willy Brandt. That panel produced a major study in 1979 of North-South economic relations and is about to release another confirming its previous gloomy assessment of the prospect of national bankruptcies, the spread of hunger and the plight of Third World countries.

"Sweden itself today is in a very difficult economic situation," Palme said, coping with the effects of the international recession, declining exports, lower industrial investment and a substantial foreign debt. "But we must stubbornly uphold the idea of spending one percent of our gross national product on foreign aid. . .with great trouble." This pledge means an annual Swedish commitment of more than $1 billion in assistance to developing countries.

Palme has also served as an international mediator. In 1980, when war erupted between Iran and Iraq, he was asked by then-U.N. secretary general Kurt Waldheim to attempt a settlement. He traveled to the region on five occasions without success, most recently last February. The time for headway was not right then to stop a "ferocious" war, he said, and "it is not right now.

"However, I still maintain my availability," he added, "in case there is a possibility for peace. The war must end sometime. It is draining the resources of both sides."

In his last period as prime minister, from 1969 until he was defeated in 1976, Palme strongly opposed the American role in Vietnam. This gave him a lasting reputation for favoring leftist liberation movements in the Third World. Yet, in commenting today on Reagan administration policy in Central America, Palme chose his words carefully, balancing criticism with advice for an alternative strategy.

Palme said he is "deeply worried about developments in Central America, the mounting repression. Some of these people being killed are old friends of mine in Guatemala, El Salvador. . .I think the Reagan administration is putting too much emphasis on military means and too little emphasis on talks and negotiations or economic and social reform. . .

"When the U.S. takes responsibility for conditions in those countries, as it has, and the repression goes on, then the United States leaves itself open to criticism."

But the American involvement in Central America, Palme quickly adds, can't begin to be compared to the Soviet role in Afghanistan, "an outright invasion. . .a terrible mistake."