A possible cessation of fighting in the Horn of Africa may do little to improve strained relations between the Soviet Union and the United States.

Soviet backing of Ethiopia in its fight with Somali invaders, is based on ideological and strategic considerations that reflect a deep commitment on the part of the Kremlin to a position of power in the Red Sea region. Soviet theoreticians and commentators have made this larger concern quite clear in recent months, especially since last November when Somali peesident Mohammed Said Barre expelled the Soviets from his country.

Writing recently in the weekly News Times, prominent commentator Vsevolod Sofinsky asserted that the present events in the Horn "are the direct result of a compact between the imperialist powers, primarily the U.S. and the reactionary Arab regimes, spearheaded against the progressive forces in the Red Sea basin."

He then described why the Soviets and United States will be quarreling for some years to come: "The area has been allotted an exceptionally important place in the imperialist strategic plans because of its geographic location at the junction of Asia and Africa, its first-class ports in the Gulf of Aden and Indian Ocean, and above all, its proximity to key sealanes linking oil-producing countries with America and Europe. Some 70 percent of the oil and other raw materials imported by Western Europe is carried over these sea routes."

Unstated but very clear is the Soviet eagerness to have a presence of some sort in that area. In a larger sense, the quarrel with the US about the Horn is seen here as having wide implications for the Mideast as well.

Sofinsky's article neatly summarizes Soviet views on this point as well. He writes that the Soviets believe "the U.S. and other "imperialist powers, operating through Egypt, Sudan and Saudi Arabia, are trying to line up an alliance of reactionary Arab regimes backed by the financial sinew of Saudi Arabia." Sofinsky said the purpose of the alliance is to divide Ethiopia and destroy the military Marxist regime there that overthrew Haile Selassie in 1974.

A similar grouping of the United States, Saudi Arabia, Israel and Egypt is plotting to keep the Soviets from playing a role in any Middel East settlement, according to other official writings. But in the Kremlin's drive for world respectability , the notion of an active role in any Middle East settlement figures prominently.

Thus, in the opinion of some Western observers here, the leadership will continue to seek leverage in one arena as a way to influence its position in another. At the same time the agreement with the United States, on strategic arms limitations and other major issue.

"There is now a thorough understanding in Washington that the Soviets will continue to compartmentalize dentene," one source said here recently. "There is a sense of almost complete frustration (in Washington) about its inability to bring about better behavior by the Soviets either in their own country or outside."

At present, the Soviet Union has successfully avoided a showdown with Western countries over its alleged violations of the human rights provisions of the Helsinki Treaty. It achieved adoption of a bland final document on that issue at the recent Belgrade conference.

Strategic arms talks are moving at a snail's pace in Geneva and there are clear divisions within the Carter administration and Congress as to how to proceed. Although the Soviets have expressed eagerness to conclude a new SALT accord, they are stead-fastly maintained that it is the U.A. that must propose changes that meet Soviet aims.

In addition, Moscow is filling with rumors that the long-expected trial of Anatoly Scharansky, a jailed human rights activist who has been charged with treason, is about to begin.

Against this background of stalled progress and Soviet intransigence, some sources here now believe it may be a considerable interval before relations between the two supers improve.

"On a scale of 1 to 10, I'd rate it a 3.5 right now," said one source.