Argentina's military government, torn by power struggles following its failed invasion of the Falkland Islands, collapsed tonight as the Army assumed sole power and named retired Gen. Reynaldo Bignone as president.

Both the Argentine Navy and Air Force, which strongly opposed Bignone's appointment, withdrew from the six-year-old armed forces government and delegated political power to the Army. The Air Force said that it would remain in the junta but that the junta would only consider matters of national security.

Political sources said the move left the military in a nearly unprecedented state of political chaos and that the Army's government could be highly unstable. They said the ongoing power struggle within the military was unlikely to end.

The Army announced its full assumption of power on national television late this afternoon after a week of bitter infighting among military leaders following the surrender of Argentine forces to Britain on the Falkland Islands.

A communique signed by the Army commander in chief, Gen. Cristino Nicolaides, pledged that the Army would install a government of "limited transition" that would seek to return Argentina to democratic government "in the shortest time possible."

The statement said that the reorganization of Argentina's political institutions and parties would be agreed upon with political leaders and other "fundamental organizations of national life" and that a transfer of power to a democratically elected government should take place no later than "the first months of 1984."

The Army also would negotiate the social and economic policies of its government with civilian leaders, the communique said. But it made no mention of the joint government of military and civilian leaders that had been proposed by civilian leaders and some military commanders.

Bignone, a 62-year-old retired division general who held the key political post of Army general secretary in the government of Jorge Videla, will take office on July 1, the Army said.

Bignone has been described as having wide contacts with political leaders and the media. He has been described by some analysts as a relative moderate within the Army. Political sources noted, however, that the most powerful figure in the Army government was likely to be Nicolaides, who took over as commander in chief following the ouster of Gen. Leopoldo Galtieri as both president and Army commander last Thursday.

Nicolaides, 52, a close supporter of Galtieri as a Buenos Aires-based corps commander, is regarded as one of the armed forces' most conservative figures for his espousal of virulent anticommunism and his open distaste for Argentina's traditional democratic leaders. Political sources said civilian leaders were concerned that they would never reach the policy agreements with the new government promised in the Army communique.

Buenos Aires remained quiet tonight as the military crisis unfolded. Although the conflict has been described as one of the most serious in Argentina's turbulent modern history, the disputes of the last week have largely taken place in the sealed headquarters of the military services, and unofficial accounts reaching the public have been fragmented and contradictory.

Most Argentines, who have seen five presidents come and go in the last 15 months alone, have ignored the military struggles and were preoccupied with radio and television broadcasts of a World Cup soccer match this afternoon when the Army interrupted with its communique.

Radio and television stations returned to broadcasting a match between Belgium and Hungary immediately after the short Army announcement, and minutes later widespread cheering could be heard in downtown Buenos Aires as a goal was scored.

Political analysts and sources said that divisions between the three armed services have been a part of military rule since armed forces commanders overturned the constitutional government of Isabel Peron in March 1976 and created what they called the "process of national reorganization."

The military government was ruled by the commanders in chief of the three armed forces serving as a junta, and directed by a president appointed by the junta who was always either the Army commander in chief or a retired Army general. Each junta member also was obliged to consult with the top rank of commanders in his service on any policy decision of importance.

This bulky structure frequently was stymied by rivalries among the services, particularly between the Army and Navy, which have competed for power regularly since the Argentine armed forces entered government for the first time in 1930.

The power struggles of the past week, as in the past, were focused on these rivalries and the perceived responsibility of military commanders for the failure of the Falklands invasion. Ideology and the future political policies of the military government were of secondary concern, sources said.

The basis of the crisis, according to sources and reports in Buenos Aires, appears to lie in the determination of a substantial group of Army commanders--some of them of the second and third rank--to force a complete reorganization of military command following the humiliating surrender by Argentine troops at Stanley.

These generals forced the resignation of Galtieri last week in a series of stormy meetings, then began pressing for the ouster of the other two junta members responsible for the invasion and the subsequent failure to reach a diplomatic settlement with Britain.

But the Navy commander, Rear Adm. Jorge I. Anaya, and the Air Force commander in chief, Gen. Basilio Lami Dozo, were backed by their services in refusing to resign, and Lami Dozo, drawing on the performance of Air Force pilots who sank five British warships, sought the presidential post for himself.

When he was staunchly opposed by the Army, Lami Dozo proposed that the junta name a civilian as president, and was later joined in this move by Anaya, who had been neutral in the presidential selection but was anxious to preserve his own position.

The proposal of the Air Force and Navy represented an unprecedented departure from traditional military politics in Argentina, where the Army has always held the balance of power because of its superior size and military strength. Argentina never has had a permanent military president who was not an Army member, and Army leaders remained unyielding in insisting that a general be named to replace Galtieri.

It was this insistence--and the Army's ability to back up its position with military force--that led the two other services to abandon the military government, sources here said.

Although both the Air Force and Navy commands technically backed the new Army government tonight, political sources said their clear opposition to both Bignone and Nicolaides could badly damage the Army's ability to reorganize the government and continue in power even as an administration of "limited transition."

According to widespread reports here today, when Bignone appeared yesterday at a meeting of the junta to explain his governmental program, he was interrupted abruptly by Lami Dozo, who said the Air Force had decided that an Army-led government was not feasible.

In addition, sources said the collapse of the old military rule had not ended the power struggles within the military. Army generals were likely to continue pressing demands that Lami Dozo and Anaya be replaced for their role in the Falklands conflict, arguing that otherwise the Army historically would be judged the only force responsible for the fiasco.