Ethiopia is seeking to repair its relations with the United States after an abrupt and bitter break of their 24-year-old alliance last April - a move that has proven costly to this country in its war against better-equipped Somali forces.

One immediate objective of the Marxist military government here is to obtain about $40 million worth of American arms that were on order or in the pipeline when it unilaterally cancelled the 1953 U.S. military assistance program five months ago.

High Ethiopian officials insist they are also anxious to strike a more balanced foreign policy after verring sharply away from the United States and toward the Soviet Union last spring. "We want to become a kind of Yugoslavia in this region and have the same kind of relations the United States has with that country," Ethiopian Foreign Minister Wolde Giorgis said in an interview.

He said that the Ethopian decision to turn toward the Soviet Union for military assistance followed a "virtual blockade" by the United States of arms to Ethiopia at a crucial moment in the country's struggle to maintain national unity. "We feel here in Ethiopia that we were betrayed (by the United States) at a critical time," he commented.

The United States provided Ethiopia with more than $300 million worth of arms between 1953 and this year, making it the leading recipient of American military assistance in black Africa.

The Ethiopians have long interpreted various treaties signed with Washington over the years as a U.S. commitment to help protect their territorial integrity against Somalia, whose forces have seized vast areas of the disputed Ogaden region in south-eastern Ethiopia.

Late last April, the Ethiopian government ordered five American facilities, including a radio relay station in Asmara and a military advisory program, closed after more than a year of steady deterioration in U.S.-Ethiopian relations. At the time, threats from Eritrean separatists in the north and Somali insurgents in the southeast were growing to crisis proportions.

There are a number of indications of the new Ethiopian desire to normalize relations with Washington, although local Western diplomats are still uncertain what it all means. Some view it as a temporary tactical move stemming from doubts about the reliability of the country's new big power backer, the Soviet Union, which also is still providing arms and technical advice to the Somalis.

The first sign of a move toward [WORD ILLEGIBLE] with the United States was the decision of the military government to ask formally in July for American economic assistance to be continued. An initial $200,000 rural development project was recently signed between the two countries and there are two more totaling about $10 million dollars in the works.

Then, in early August, the government ordered the local media to stop attacking "American imperialism" and calling the United States the prime enemy of the country and its three-year-old socialist revolution.Everyone from the chairman of the ruling military council, Lt-Col. Mengistu Haile Mariam, downwards has taken since to using the term "international imperialism" and attacking the "reactionary Arab regimes" aiding Somalia.

Western diplomats here report that Ethiopian leaders also have changed their attitude toward them and now are opened expressing interest in good relations with both the West and the East and in not being tagged as a Soviet "puppet."

Finally, the decision to allow some Western journalists into the country - including this reporter, who was expelled together with two other resident correspondents last April - is taken here as an indication of Ethiopia's wish to keep the door open to the West.

The effort to establish normal relations with the United States has included a decision to send a new ambassador to Washington after more than two years without one there and a series of meetings between several high Ethiopian military officials and two American envoys, Paul Henze, a staff member of the National Security Council, and Richard Post, the State Department's director for East African affairs.

The two men, who recently toured Ethiopia, Somalia, Kenya and Sudan, held talks in Addis Ababa two weeks ago with both the foreign minister and Col. Berhanu Beyeh, the top military council member in charge of Ethiopia's external affairs.

Their talks were understood to have centered on the future of U.S.-Ethiopian relations in general and the possibility of the United States releasing some of the arms Ethiopia had ordered and partly paid for before last April's break.

The arms in question, according to Ethiopian military sources, include eight F-5E fighter aircraft, 14 M-60 havey tanks, 330 jeeps and 45 trucks, about 50 armored personnel carriers, three swift patrol boats and the armament for four others, and anti-tank missiles.

The sources said Ethiopia had paid out around $40 million for the arms but they had been blocked from leaving the United States after the April rupture. They acknowledge, however, that Ethiopia also owed the U.S. government about $30 million on arms bought on credit. This, they said, left a balance of about $10 million in Ethiopia's favor in the outstanding U.S.-Ethiopian arms sales dispute.

The Ethiopians are understood to be particularly anxious to get the second squadron of F-5Es, an aircraft that has proven extremely effective in dogfights with Somali's MIG-21s and in attacks on Somali-armored columns. The better ability of Ethiopian pilots has also been a key factor, according to Western and Ethiopian sources.

In addition, the Ethiopians badly need spare parts for their American aircraft, some of which have been obtained through Israel. The Israelis are also reported to be providing some maintenance crews for the F-5s.

The newly-named ambassador to Washington is Ayalew Mandefro, a Tuft's University graduate who has been Ethiopia's Defense Minister for the past 2 1/2 years. In an interview, he defended Ethiopia's cut of military ties with the United States, saying that Washington had begun dragging its feet on his country's arms requests as far back as 1973 despite the massive build-up of Soviet arms in Somalia.

He charged that the United States, in effect, had initiated the break by not responding to his country's growing military needs in the face of the mounting separatist movement in the northern province of Eritrea and of the Somali-backed invasion of Ogaden.

Shortly before the rupture, he said, Ethiopia had asked for around, $60 million of ammunition and acceleration of the delivery of the arms it had ordered. "This crucial equipment was not-delivered at a crucial time for us," he said.

In an obvious attempt to answer allegations by the Carter administration of serious human-rights violations by the military government, both Mengistu and his foreign minister have stressed that it was doing everything possible to assure the country's 30 million peasants and workers of these rights.

Mengistu is understood to be under considerable pressure from more moderate elements in the military council and the officer corps to mend ties with the United States to restore, partially at least, the flow of American arms to give Ethiopia a more non-aligned image.

The abrupt manner of the break with the United States, which created much bitterness on both sides, is now described openly by many Ethiopian officials as "regrettable," "a mistake."

"Let's be honest," said one Ethiopian official. "We both made mistakes in the past and now we want to correct this."