Out of the horn of Africa there comes a tricky challenge that is dividing the White House and State Department. The Russians are pouring military supplies, experts and Cuban soldiers into Ethiopia at a great rate.

But the Russians have been invited in to help Ethiopia defend itself against groups and countries friendly to the United States. So the issue is whether to challenge the spread of communism on the Big Two level, as the White House prefers, or to follow the State Department formula of influencing local conditions in ways that make it easy for the Ethiopians to despense with the Russians.

Behind all this is the chain of events set in motion in Ethiopia by the revolution of 1974. A group of military officers, the so-called Dergue, drove Emperor Haile Selassie from power. They promised important social reforms and enjoyed unquestioned popularity at first.

But the Dergue has found it hard to connect its social impulses with such traditional Ethiopian institutions as the Coptic church. Feuding among different factions in the Dergue has yielded in Addis Ababa what wo visiting congressmen - Don Bonker (D-Wash.) and Paul Tsongas (D-Mass.) - in a fine report liken to a reign of terror.

Trouble at the center has stimulated long-standing secessionist tendencies on the edges of Ethiopia. In the heavily Moslem north, Eritrea, a secessionist movement has practically broken away from Addis Ababa. The Eritrean secession is heavily backed by Moslem countries - notably Saudi Arabia, Egypt and, at least until recently, the Sudan.

Ogaden province in the south has been the scene of a combined insurrection and war. The troublemarkers are ethnic Somalis, who make up most of the population of Ogaden, reinforced by troops from Somalia, which considers Ogaden part of its territory.

For Russia, the horn provides a gate way from the Red Sea to the Persian Gulf and Indian Ocean and a bridge from the Middle East to Africa: Soviet aides built up a strong Somali army from 1970 until 1976, and in return the Somalis gave Russia a base at Berbera on the Indian Ocean. But when Moscow began helping Ethiopia earlier this year, the Somalis expelled the Russians and turned to the anti-Communist Arab countries and to the West for help.

The American connection with the horn originally ran through Haile Selassie. This country provided the basic weapons and training for the Ethiopian forces and originally favoured their control of Eritrea and the Ogaden. American relations with the Dergue, however, have turned sour, and this country has cut aid and seen its military installaions closed down.

Now the Carter administration is under heavy pressure to block further Soviet penetration in the horn. The obvious way is to challenge Russia at the great-power level, intimating darkly that further hanky-panky in the horn will generate a tough U.S. response and perhaps prejudice negotiations for an arm-control accord. Unfortunately, the backers of the revolt in Eritrea are close to Washington, and President Carter himself, by overt backing of the Somalis, contributed not a little to the fighting. Most of the African countries, fearing that dismemberment of one would lead to a tribal breakup of all back Ethiopia. So there is every chance the Russians would simply ignore a warning.

A more judicious approach is advocated by the State Department and Bonker and Tsongas. Their idea is that Somalia pull back its forces in the Ogaden and ask for peace negotiations. Some arrangement might then be worked out whereby Eritrea and the Ogaden were given local autonomy. The integrity of Ethiopia (and other Africa states) would be saved, and the Dergue could then invite the Russians out as Anwar Sadat did in Egypt. The trouble there is getting the Somalis to step back. The regime of President Said Barre apparently believes it can whip the Ethiopians and their Cuban and Russian allies. So presumably there will have to be some test of force before diplomacy can come into action.

If so, the interest of the United States is to stand clear. When the United States steps up to the plate to challenge the Russians, it ought to be able to hit the ball out of the park. Washington should not challenge the Russians all the time anywhere, no matter how ambiguous the case or uncertain the American interest. That is a recipe for batting 100 - or rather for weakening American prestige in the name of building it up.