At 6 a.m. last Friday a press agency dispatch, clattering across a teletype in the State Department Operations Center, brought the U.S. government unsettling news from Uganda. A state radio broadcast there said president Idi Amin had summoned all Americans to meet with him and ordered his security forces to stop any of them from leaving the country.

Within minutes senior State Department and White House officials were notified and within two hours President Carter and his administration were intensively at work on their first potential crisis overseas. To a large degree it was a personal challenge to Carter, who two days before in a televised press conference had roundly denounced the "horrible killings" in Uganda that "have disgusted the entire civilized world." Now the lives of Americans as well as Africans seemed to be at risk in the grip of the unpredictable, despotic Amin.

In the hours and days that followed, the worldwide apparatus of the U.S. government was wielded in quiet but concerted fashion to protect the 240 or so Americans in Uganda from harm. Both the diplomatic and military sinews of U.S. power were flexed in ways that must have been unmistakable to Amin but which did not result in a public confrontation.

In keeping with the low-key nature of the U.S. response, the episode that began last Friday has been called in the White House "a problem" rather than "a crisis." Because the Americans are still at risk, Carter has ordered that there be no crowing over the results and no boasting by officials of what the United States said and did in the week just past. Nevertheless, enough is known to sketch the outlines of the story - and to draw a few conclusions about the new administration's handling of a dangerous challenge.

From the beginning the critical problem for the United States was the unpredictable nature of Amin and his rule. The government did not assume it was dealing with a reasonable man and could not even be certain it was dealing with a national one. Thus the basic guideline adopted within first hours after last Friday's announcement was not to overreact. The United States determined to use its influence without placing Amin or those associated with him in a difficult public position.

Following customary practice a special working group composed of State Department, Defense Department, Central Intelligence Agency and U.S. Information Agency officials was organized Friday morning to coordinate government action on a round-the-clock basis. Eventually about 25 officials would be involved in this, under the chairmanship of Assistant Secretary of State for African Affairs William E. Schaufele Jr., the government's senior expert on the region.

Placing State and Schaufele in charge - rather than convening the National Security Council or moving the action to the White House - was part of an early decision to treat "the problem" with restraint.

On personal instructions from Carter, White House and State Department spokesmen expressed "concern" about Americans in Uganda. Presidential press secretary Jody Powell added, "It is safe to assume the President will do what is both necessary and proper to protect American lives anywhere." But the manifestations of governmental crisis - emergency meetings of grim-faced officials and officials racing for airports - were deliberately avoided.

An immediate decision taken at the State Department was to get word to Amin, in ways that would make an impression on him, that the United States considered treatment of its citizens an extremely serious matter. To send the message directly, Schaufele called in Washington, Paul C. Chepkwurui. Simultaneously, the United States sent official word through Bonn to the West German ambassador in Kampala, who had represented U.S. interests in Uganda since Washington closed its embassy in November, 1973.

A more circuitous but probably more impressive route for the U.S. message through the leaders of close to 10 other countries, mostly in Africa, which have friendly relations with Uganda. Through U.S. ambassadors and occasionally other channels, these leaders were asked to tell Amin that they shared Washington's concern about the welfare of American citizens and to express the hope that any who wished to leave Uganda would be permitted to do so.

At Entebbe airport, where Amin planned to meet the Americans before a crowd of 3,000 people, personal emissaries suddenly began arriving from the Presidents of the Sudan, Zaire and Rwanda, all neighboring countries of great importance to Uganda. Amin, who is a Moslem, was handed a personal message from Saudi Arabian Crown Prince Fahd, the operating leader of this premier Moslem nation.

Among other nations that sent messages were such conduits as the Central African Empire, whose President Bokassa admires Napoleon and recently proclaimed himself Emperor Bakassa I, and Somalia, which, like Uganda, has been a major recipient of Soviet military aid. So many messages were recieved so quickly that Amin complained, "some African leaders have become telephone operators and messengers of America."

One message the United States did not want delivered with its national at risk was further official condemnation of Amin. The Senate Foreign Relations Committee had unanimously condemned Amin's rule and Ugandan murders in a committee meeting Feb. 22. But last Friday morning, within hours of Amin's challenge to the United States, Secretary of State Cyrus R. Vance telephoned the resolution's sponsor, Sen. Clifford, Case R(N.J.), in a successful appeal to avoid further action on the condemnation for the time being.

Along with the diplomatic activity, the United States sent a military message through the 2 activities of a fourhip nuclear-powered task-force which by chance had been cruising near Uganda in the Indian Ocean. The aircraft carrier Enterprise and nuclear attack submarine Tautog had left after calls in the Kenyan port of Mombasa on Wednesday, Feb. 23 - just two days before Amin's challenge. Instead of steaming back to Asia as earlier planned, the U.S. task force was ordered to remain in the Indian Ocean within easy aircraft range of Uganda.

There is no public indication that a U.S. military response was seriously considered. It is known that officials discussed the unhappy precedent of Stanleyville, late in 1964, when U.S. aircraft landed Belgian paratroopers to free American hostages from the Congo - leaving 20 hostages dead in the process. It is reported that last Friday two U.S. naval intelligence officers flew to Israel to see planners of that country's more successful experience in freeing hostages at Entebbe Airport last July.

Carter said little in public and did the minimum which it felt was necessary to convince Amin not to rifle with Americans in his country. When the Uganda announced early Tuesday that Americans are free to leave, the United States greeted this with mild statements of approval and a terse message to Amin from Carter.

Though "the problem" had faded for the moment so far as Americans are concerned, reports of continuing massacres with Uganda indicate a highly unstable and unpredictable situation.

"You wonder if this is over or if this is just the beginning," said Sen. Dick Clark (D-Iowa), a leading African expert in Congress. Clark pointed out that Amin's U.S. challenge diverted attention from the massive human rights problem which Carter spoke of 10 days ago.

Despite new reports of extensive massacres, received by the United States both from prominent newspaper stories and diplomatic sources, the State Department refused to comment yesterday on grounds that the killings in Uganda are "uncomfirmed."