Both Cuba and the United States took small steps back from weeks of mutual antagonism here today and indicated hopes for a reduction in tensions.

In a front-page editorial in Granma, the Communist Party newspaper, Havana allowed what seasoned watchers agreed was the first cryptic break in the tone of what have been unrelenting attacks against the United States and the Carter administration.

"We have nothing personal against Carter," the editorial said, asking rhetorically about guarantees that the United States would address longterm issues between the two countries if the problem of the tens of thousands of refugees herded into the United States could be solved.

Wayne Smith, chief U.S. diplomat here, said in a briefing for reporters that he believes the anti-American campaign here "has abated dramatically" following its culmination in Saturday's march of an estimated million Cubans past the U.S. mission.

"It's certainly no secret that U.S.-Cuban relations are strained at the moment," smith said, "but I think if we can talk about our problems it will clear the atmosphere . . . Hopefully the two sides can begin to discuss some of the problems."

However slight, these steps were viewed here as the first glimmer of a possibility that the two countries have begun to back away from escalating tensions to at least a frigid status quo.

In contrast to recent government propaganda aimed at a domestic audience, today's editorial in Granma appeared directed abroad.

After recounting Cuba's version of the past 20 years of "U.S. aggression," it admitted that many Cubans, as in other Third World countries, want to leave home for economic reasons, stemming, Granma said, from U.S. perpetuation of world economic inequality.

The editorial said Cuba in the past has been willing to discuss "partial solutions" to bilateral issues while letting its larger gripes with the United States slide.

It is those questions -- the U.S. economic blockade, the U.S. naval base at Guantanamo and overflights by U.S. spy planes -- that Cuba wants to discuss. While it saw little hope of success in the past, Cuba now views the issues of nearly 400 refugees in the U.S. diplomatic mission here and the exodus from Mariel, as providing a rare chance to bargain effectively with the United States.

"We understand that the United States is right in the middle of its demagogic electoral campaign," the editorial said. "But the problems of a small neighbor country also have to be understood by a large and powerful state that is vacant of principles and whose government is vacant of morals."

"Ronald Reagan is an extreme reactionary," it said. "No one could suppose that we are against Carter and for Reagan."