Falklands: British resolve, US diplomacy; Haig will shuttle between London, Buenos Aires

The United States is moving swiftly into place as chief mediator between Britain and Argentina over the Falkland Islands, while the potential combatants step up their hostile sparring.

President Reagan, off to the Caribbean for a working vacation, is sending Secretary of State Alexander M. Haig Jr. to London and Buenos Aires on negotiating missions, the White House announced.

Mr. Haig was to have accompanied the President on his trip to Jamaica and Barbados, where Mr. Reagan will discuss his Caribbean Basin initiative with local leaders.

Announcement of the Haig mission follows talks between the secretary of state and three diplomats directly involved in the Falklands dispute - the Argentine foreign minister and the ambassadors to Washington of Britain and Argentina.

At the State Department, meanwhile, a special working group centered in the department's operations room has been monitoring the Falklands crisis since April 2.

White House spokesman David Gergen backed off from describing the US role as ''mediation,'' but called it ''an effort to be of assistance'' in the avoidance of bloodshed.

The Reagan administration, with close ties to both disputants, is walking a diplomatic tightrope of neutrality, especially on the core issue of sovereignty over the Falklands.

Argentina, which invaded the islands with 4,000 troops last week, asserts that Britain illegally seized the Falklands by ousting an Argentine garrison in 1833.

London claims unbroken British sovereignty in the islands for the past 150 years and notes that almost all of the 1,800 Falkland Islanders are of British stock.

While this US shuttle diplomacy emerged, the Falklands crisis took on wider dimensions:

* Argentina's original invasion force was bolstered by fresh troops and by airlifts of arms from the Argentine mainland.

A bevy of Argentine military, political, and labor leaders -including some opponents of the regime led by President Leopoldo Fortunato Galtieri - flew to the Falklands for the swearing-in of Mario Menendez as governor of the islands.

* France, reaffirming its support for Britain, banned are shipments to Argentina, including fulfillment of contracts ''concerning aircraft and antiaircraft missiles.''

French President Mitterrand made a personal telephone call to British Prime Minister Margaret Thatcher, under fire domestically for her handling of the crisis, to reassure her of French backing.

* At least two more of Britain's European Community partners - Belgium and West Germany - reportedly curtailed or cut off arms sales to Argentina.

* London, meanwhile, banned imports of goods from Argentina and asked its nine Common Market partners to do the same. This followed London's diplomatic break with Buenos Aires, the freezing of Argentine assets in Britain, and an end to British export credits benefiting Argentina.

The sword of economic warfare is double-edged, for British firms have substantial assets in Argentina. Also, the South American nation reportedly owes British banks nearly $6 billion, a sum far greater than the value of Argentine assets available to be seized in Britain.

Finally, about 17,000 British subjects live in Argentina. They are being urged by London to leave the country.

Both Britain and Argentina - tingling with national pride, either wounded or exuberant - have edged themselves well out on limbs and it is Secretary Haig's job to find a formula that will pull them back, short of war.

British officials claim no mediation would be acceptable that left the Falklands under the Argentine flag. Argentina, with its troops on the scene and the nation broadly united behind the Falklands adventure, says that the issue of sovereignty is not negotiable.

Both powers, however, indicate that they prefer a peaceful solution, which gives Haig, backed up by President Reagan's proffered role as ''honest broker,'' an opening.

Haig races against time, as the large British armada of heavily armed ships steams its way down and across the Atlantic to the remote Falklands.

The hope is to find a diplomatic solution before Argentine and British guns come within each other's range, with all the risk that would entail.

Latin American governments, meanwhile, appear to be torn between their instinctive loyalty to a fellow Latin nation and their concern that the Falkland crisis could lead to war.