The United States has sponsored an unpublicized, yearlong feeding program in rebel-held areas of northern Ethiopia by way of Sudan, and soon will ask the new Sudanese military government for permission to expand the effort.

Working through private relief agencies, the Agency for International Development already has approved 115,000 tons of food and 86 trucks for the operation.

The effort has become a delicate issue within the Reagan administration because of its implications for already uncertain relations with pro-American Sudan and Soviet-backed Marxist Ethiopia.

The new military government in Sudan has expressed a desire to improve relations with Ethiopia, and U.S. officials fear that too much publicity over a food operation in cooperation with the United States could lead Sudan to scuttle the program.

Also, the United States is in delicate negotiations with the Ethiopian government to allow the food to flow into the rebel-held territory through normal channels within the country, and officials say they fear that those negotiations could fail or, worse, that the Ethiopians might declare the Sudan border-crossing a hostile act and attack the relief convoys or even raid staging points in Sudan.

The U.S. operation may have implications for U.S. contact with other rebel groups around the world.

"It holds precedents for Afghanistan and Nicaragua," said a senior administration official. "Is it legal to give humanitarian assistance to rebel groups across an international border?"

Administration officials involved in U.S. efforts to help the Afghan rebels and Nicaraguan "contras" are said to be watching the Ethiopian cross-border operation with particular interest because of its potential as a precedent for similar U.S. operations.

In addition, there is widespread agreement among U.S. policy-makers and private volunteer groups involved in the operation that the situation in the two war-torn northern provinces of Ethiopia -- Tigray and Eritrea -- has a potential for the explosive mix of humanitarian aid and politics that marked the bitter and bloody struggle farther south in Biafra.

"It's the exact same issue," said Fred Gregory, a director of Mercy Corp International, which has been involved in the cross-border operation. "The same thing happened in Biafra."

Biafra was the short-lived, self-declared state in eastern Nigeria where a bloody secessionist struggle was fought in 1967-70 and where private U.S. volunteer groups became deeply involved in trying to save starving noncombatants. The relief groups sided with the Ibo tribesmen of Biafra and lobbied on their behalf in the United States.

Today as then, a number of private relief groups are pressing the U.S. government to take a more active role in Ethiopia. AID and State Department officials estimate that roughly 2.3 million people are "in need" of assistance in northern Ethiopia.

Many U.S. and private relief officials say that about 200,000 in Tigray and 50,000 in Eritrea soon will die of starvation.

A senior administration official said the situation in northern Eritrea has the makings of "one of the great tragedies of modern times."

AID and State Department officials say that even a "safe passage" agreement allowing private groups to enter the rebel-held areas from Ethiopia, coupled with an expanded cross-border operation, would reach only about 1 million out of the 2.3 million in need because of rough terrain and massive logistical problems.

One of the main differences between the U.S. government role in Biafra and in northern Ethiopia is that Washington never became involved even indirectly on the side of the Ibo rebels in Nigeria.

The danger is far greater today that the United States will become entangled at least indirectly in the Eritrean conflict, which pits secessionist groups against Ethiopia's Soviet-backed Marxist government.

This is partly because many high-ranking Reagan administration officials have come to the conclusion that it probably is impossible for the United States to establish a working relationship with the antagonistic Marxist regime.

In addition, there is mounting humanitarian concern about the several million drought-affected people in northern Ethiopia who still have not benefited from the international relief pouring in.

AID officials maintain that they are taking careful steps to prevent any direct contacts between the U.S. government and the rebel groups in either Eritrea or Tigray mainly by working through international and private relief groups.

The main conduits for U.S. assistance have been New York-based Lutheran World Relief and Mercy Corps International in Seattle. But AID now has asked CARE in New York to take over the logistics of transporting all the U.S. food aid from Port Sudan to the Ethiopian border.

AID also has been funneling some of its emergency relief supplies through the Geneva-based International Red Cross, which is working in Addis Ababa, the Ethiopian capital, as well.

The Lutherans and Mercy Corps depend mainly on two local private groups, the Eritrean Relief Committee (ERA) and the Relief Society of Tigray (REST), to truck the food by night into the rebel areas.

The ERA is affiliated with the main Marxist-oriented Eritrean guerrilla group, the Eritrean People's Liberation Forces, and REST with the Tigrean People's Liberation Front.

A few weeks ago, the State Department and AID approved an additional 45,000 tons of food aid for the cross-border operation, bringing the total to 115,000 tons since October. Of this, 60,000 tons already are there or on the way, according to one AID source.

The private relief groups have asked AID for a total of 200 trucks to speed the delivery of the emergency U.S. food into the rebel-held areas. But AID and State Department officials have concluded that only about half this number can be put to effective use before the rainy season starts in June, making most roads impassable.

Despite efforts to remain outwardly "neutral" in the Ethiopian conflict, U.S. officials readily concede that they cannot directly monitor the food distribution inside rebel areas to be sure it is going to noncombatants rather than guerrillas and their families.

In addition, they admit that one of the intended effects of the food aid is to help stop the outflow of Ethiopian refugees into drought-stricken and politically unstable Sudan. Already, the 750,000 Eritreans and Tigreans gathered in camps there are a major burden on the Sudanese government's meager resources.

Thus, one impact of any expanded cross-border operation would almost certanly be to strengthen rebel forces by helping to keep their partisans and civilian supporters inside Ethiopia.

But AID and State Department officials argue that keeping the population at home is crucial to any chances of inducing farmers to sow for a new harvest in the summer rainy season.

Otherwise, they say, Sudan will be faced with a continuing influx of refugees and a huge permanent Ethiopian population living on handouts in the camps for the next two years.

When the U.S. government first became involved in the cross-border feeding operation in early 1984, AID lawyers reportedly agonized for some time over its legal implications.

Today, they are satisfied it is "within the international understanding" of what is acceptable in helping people in an "emergency humanitarian situation," the senior administration official said.

The problem is that the central government in Ethiopia takes a far different view and insists that all aid come through Addis Ababa and be distributed under its auspices.

The United States and two private American relief groups -- World Vision and Catholic Relief Services -- are seeking Addis Ababa's permission to take food into rebel-held areas.

But the prospects for such an agreement, despite earlier hopes, have been receding, according to U.S. officials.

Still, it is widely agreed that far more famine victims could be reached from the Ethiopian side of the war lines because the logistics of transporting food into northern Ethiopian are far simpler from Ethiopian ports and across its all-weather roads.

According to private relief groups and U.S. officials, plans for stepping up the cross-border feeding were discussed in early March in Khartoum by Sudanese security authorities and U.S. government aides, including AID director M. Peter McPherson and the assistant secretary of state for African affairs, Chester A. Crocker, who accompanied Vice President Bush on his African tour.

An agreement was reached in principle then and further talks about the details of an expanded operation were held with former Sudanese president Jaafar Nimeri during his visit here two weeks ago. His April 6 overthrow by a military coup, however, has left doubt about whether the Sudanese government is still in agreement.

U.S. officials say they believe Sudan will give its assent, if only to stem the continuing exodus of Ethiopian refugees trekking across the border at a rate of 2,000 to 4,000 a day.

The U.S. officials say they now are awaiting a chance to meet with members of the new ruling military council to obtain their approval and get the expanded operation under way.