With the Falklands crisis at the edge of warfare, the Reagan administration sought yesterday to get Secretary of State Alexander M. Haig Jr.'s stalled mediation effort moving again, while making clear that the United States will side openly with Britain if the dispute erupts into heavy fighting.

Administration officials said privately that strong efforts were under way to get indirect British-Argentine negotiations going on a U.S. peace proposal by having Haig resume his shuttle diplomacy with a trip to Buenos Aires by the weekend.

Despite indications yesterday from Buenos Aires that Argentina's military government had rejected the idea of a Haig visit, the Argentines made it known that they are still leaving the door open to a possible new mediation effort by Haig.

Argentine Foreign Minister Nicanor Costa Mendez paid a call on Haig at the State Department and said afterward that he had come specifically to inform the secretary that his government had not rejected the idea of a Haig trip, that the U.S. plan "is under examination and analysis" and that the possibility of continued U.S. mediation "is not discarded."

At the same time, officials in a number of government agencies expressed the view that a new military confrontation is now more likely than a last-minute diplomatic solution. At a breakfast meeting with reporters yesterday, Norman Bailey, director of planning for the National Security Council staff, said "the two countries are heading toward a generalized conflict."

Other officials said that while no final or specific decisions have been made by President Reagan, there is widespread agreement within the administration that if new fighting breaks out, the United States would no longer have anything to gain in Argentina by trying to play the neutral mediator and everything to lose in Britain, especially in public opinion there, by appearing to be an unreliable ally.

Since the outset of the crisis on April 2, U.S. officials have acknowledged privately that all-out warfare would force the United States to "tilt" toward Britain. The administration continued yesterday to avoid publicly taking sides to preserve its potential mediator role. But there was a stronger disposition in private--possibly as a means of exerting pressure on Argentina--to leave no doubt about what the United States will do if war cannot be averted.

The officials said they did not expect U.S. support for Britain to take the form of military involvement, although some American naval logistics and supply help is possible. Instead, they said, the main U.S. effort probably would be to join the economic embargo imposed against Argentina by Britain and its partners in the 10-nation European Economic Community.

These sources said the State Department has prepared a detailed chronology of the Falklands crisis, beginning with Argentina's April 2 seizure of the islands, which would be made public to demonstrate how the administration attempted to act as an "honest broker" and how its recent efforts have been rebuffed by President Leopoldo Galtieri's government in Buenos Aires.

As of last night, however, the administration was still hopeful that, despite the short time remaining before a clash proves unavoidable, the Argentines will pick up anew the U.S. proposals and get back into serious negotiation with Haig as intermediary.

The U.S. plan was worked out on the basis of Haig's findings during his shuttling between London and Buenos Aires. During talks here last week, British Foreign Secretary Francis Pym, while not committing London to accept the U.S. plan, gave Haig the go-ahead to approach the Argentines with it.

The original U.S. timetable had envisioned working out arrangements for a new Buenos Aires trip during a meeting between Haig and Costa Mendez set for last Sunday. Earlier that day, however, the British attack on South Georgia island caused Costa Mendez to cancel the meeting and announce that his country could not negotiate with Britain for the time being.

Instead, Argentina put its emphasis on inducing a special meeting here of the Organization of American States to pass a resolution supportive of its position. While the OAS meeting dragged on into the early hours of yesterday, news reports from Buenos Aires quoted unidentified Argentine diplomatic sources as saying that Haig's request to go there had been rejected.

That was disputed by State Department spokesman Dean Fischer who said yesterday that Haig, while willing to be of service to both sides, had not asked to be received in Buenos Aires. Fischer also said the U.S. proposals were under study by both Britain and Argentina and that neither country had turned them down.

He said: "We are awaiting a response. There is no ultimatum, no deadline other than what is imposed by the reality of the situation."

Then Costa Mendez, following his half-hour meeting with Haig, said that the reports from Buenos Aires were erroneous and that the U.S. plan and the possibility of a Haig trip were being weighed by his government.

The minister said he could not say when Argentina might respond to Washington. But he noted pointedly that in the OAS resolution, adopted early yesterday over U.S. objections, Haig's efforts are "mentioned as one of the roads to a possible solution, and this one is not discarded."

U.S. officials believe that, if the diplomatic momentum is not restored in the next couple of days, new military action could occur this weekend, because of Britain's stated intention to put an air blockade around the Falklands and because of signs that Argentina is deploying its fleet "recklessly."

The Argentine naval commander, a member of the ruling junta, is viewed here as the most aggressive and thus the most dangerous of the leaders in Buenos Aires in terms of averting further fighting.

Sources here said there were indications Argentina had sent one of its three submarines into the 200-mile "exclusion zone" that Britain has declared around the Falklands. Informants also said they had little doubt that the British had already landed small commando teams on the islands to scout Argentine positions, a tactic used in the recapture of South Georgia.