The tiny Falkland Islands may be far away and obscure, but their seizure by Argentina plunges the United States into a maelstrom of conflicting interests.
An outraged Britain, whose Union Jack has flown over the Falklands -- called the Malvinas by Argentina -- since 1833, expects firm diplomatic support from the United States, London's closest ally.
Such support, however, could cost Washington dearly throughout Latin America, if the British fleet now steaming toward the South Atlantic engages Argentina in war.
All this comes at a time when the Reagan administration is striving to obtain Latin backing for its controversial efforts to seal off Communist influence in Central America.
Against this background President Reagan offers to serve as an ''honest broker'' between Britain and Argentina, in the hope of averting war between the two nations.
Both of the contending countries, Mr. Reagan told reporters Monday, ''are friends'' of the United States and he expressed hope that the issue could be resolved short of the use of force.
Earlier a State Department spokesman said that the US has offered its ''good offices'' as a mediator, but that no formal American proposals have yet been forwarded to either side.
Because it will take the British task force two weeks to reach the Falklands, US diplomats have a window of time in which to try to move the crisis from potential armed conflict to the negotiating table.
Central to American diplomatic strategy is neutrality on the key issue of sovereignty over the Falklands, which are claimed both by Britain and Argentina.
Successive governments in Buenos Aires have claimed that British forces wrongfully seized the islands, when they ousted an Argentine garrison 149 years ago.
Argentine President Leopoldo Galtieri asserts that the invasion simply restored to Argentina what is rightfully hers.
A possible compromise discussed by diplomats would grant international recognition of Argentine sovereignty over the Falklands, while allowing the 1, 800 islanders the right to remain British subjects, if they so chose.
The United States has separate treaty commitments with Britain and Argentina, but these commitments are unlikely to be invoked by the Falklands crisis, officials say.
Article 5 of the NATO Treaty stipulates that ''an armed attack against one or more (NATO members) in Europe or North America shall be considered an attack against them all,'' committing North Atlantic Treaty Organization members to assist the party attacked.
The Falklands, however, lie outside the geographic limits which the NATO Treaty of 1949 defines. Britain's partners, including the United States, would not appear to be automatically bound to come to Britain's aid.
The Inter-American Treaty of Reciprocal Assistance of 1947, called the Rio Treaty, says that ''aggression against one American state shall be considered aggression against all American states'' and defines a variety of peace-keeping measures to be employed, when a member state has been attacked.
Trade sanctions and other agreed-upon limited measures, said a State Department official, are obligatory upon members in support of an aggrieved party. However, he said, the treaty -- as subsequently interpreted -- does not require a member state to engage its military forces in defense of another.
To what extent the disputed issue of sovereignty over the Falklands might affect the operation of the Rio treaty is not yet clear, according to a state department official.
Beyond the formal language of treaties, the White House wants to do nothing to offend Britain, which has been supportive of US foreign initiatives.