Argentina's military government, while quickly attempting to consolidate its political and military hold over the Falkland Islands, has signaled clearly its hopes of heading off the oncoming British war fleet through the diplomatic leverage of Latin America and its newly warm friendship with the United States.

Officials here appeared to be basing their hope of retaining possession of the long-disputed islands on U.S. mediation and pressure against British militancy. Argentine Foreign Minister Nicanor Costa Mendez met in Washington with the Organization of American States and high-ranking U.S. officials.

With nearly 150 years of patriotism at stake, there appeared to be little prospect that Argentina would agree to retreat from the Falklands--which are called the Malvinas here--even in the face of an imminent British attack.

Argentine Interior Minister Alfredo Saint-Jean, who is scheduled to fly to the islands Wednesday to swear in the military governor for what Argentina has designated its 23rd province, told reporters here today that "in a civilized world . . . one cannot think of a decision" by Britain to retake the Falklands by force. Saint-Jean also expressed confidence that Argentina would be strongly backed against Britain by the Latin American members of the OAS.

Argentine officials have appealed for regional support by arguing that the seizure of the British-controlled islands represented a reversal of nearly 150 years of colonialism and by frequently invoking the Rio Treaty, which commits Latin American nations and the United States to consult in the event that one of them is attacked.

So far, however, the government clearly has been disappointed by its failure to obtain the level of international support it expected. In particular, officials were surprised when the Soviet Union failed to veto a Security Council resolution Saturday calling for an Argentine withdrawal from the island and nonaligned members of the council failed to back Argentina's position.

Although the governments of Venezuela, Peru and Uruguay have expressed support for Argentina's occupation, other Latin American powers appear to be hesitating. Chile, concerned about its own volatile border dispute with Argentina, has been quietly critical of the operation, while Brazil has opposed Argentina's use of force and has hinted that it might allow British warships to refuel in its ports.

As a result, Argentina has increasingly come to turn its hope for a successful end to the crisis to the United States, reports and sources here said. In the past year, both governments have sought actively to establish close relations, and Argentina, which has backed U.S. policy in Central America politically and with offers of arms, believes that the United States now should return the support, officials here said.

Argentina appears to hope that the Reagan administration, unwilling to oppose directly its carefully courted Latin American ally, will be able to prevent fighting and encourage negotiations that will leave the Falklands in the hands of Argentina at least while talks drag on.

Meanwhile, the government has moved to consolidate its military hold on the islands, reinforcing the Falklands' defenses with troops and armor and reportedly nearly vacating several mainland military bases, while arguing that the British could not forcibly retake the island without inflicting heavy civilian casualties.

Argentina also announced this morning that it had captured seven more British Marines on the Falklands, after the soldiers had escaped into the interior of one of the islands during Friday's attack. The Marines, who according to reports here spent the weekend hiding in a cave, were not harmed during their capture, officials said.

While military preparations continued, the mood of apparent jubilation that swept Buenos Aires after the Argentine operation against the island clearly had turned today to deep concern about the possibility of a British military attack.

Newspapers headlined the departure of the large British naval force on a mission to restore British control to the Falklands, and the government announcement of triumph in the islands 300 miles off the coast turned to reports of blackout measures to be implemented Wednesday in the Falklands and the Argentine port of Commodoro Rivadavia, where many military and supply operations are based.

In the Falklands, conditions were said to be tranquil and normal for the island's 1,800 predominantly English-speaking residents, who were placed under a series of tough restrictions shortly after Argentine troops arrived.

A Foreign Ministry official said today that rules requiring residents to remain in their homes had been at least temporarily relaxed, and the kelpers, as Falkland residents are called, attended church yesterday and had gone back to their regular routines today.

Sixty Argentine journalists who were flown by the military to the islands to report on conditions had returned by this morning, and a military spokesman said there were no plans to permit journalists or others to travel to the territory.