Argentina has presented Secretary of State Alexander M. Haig Jr. with a detailed proposal to settle the dispute with Britain over the Falkland Islands. The proposal skirts the formal issue of sovereignty over the islands, but would give Argentina the key administrative role in ruling them, according to sources.

Informants here say the proposal, in writing, contains a number of points known to be unacceptable to London.

Nevertheless, they say, it may be the first actual "piece of paper on the table" that the two countries and the United States have to work with in trying to find a peaceful solution to the crisis. Sources here stress that the United States has not endorsed the new proposal.

A State Department spokesman declined to comment on any aspect of the continuing mediation effort.

Reportedly signed by Argentine Foreign Minister Nicanor Costa Mendez and given to Haig shortly after his arrival in Buenos Aires Thursday evening, the proposal is understood to call for Britain and Argentina to withdraw their military forces from the region during a two-week period.

Yesterday, Haig and Argentine officials exchanged written proposals for resolving the dispute, and Haig delivered a note from President Reagan to Argentine President Leopoldo Galtieri. After six hours of talks, officials were cautiously optimistic that a diplomatic solution to the crisis can be reached. Details on Page A16.

Under the Argentine plan, the more than two dozen Royal Navy surface ships sailing toward the Falklands and British submarines already around the islands in the South Atlantic would withdraw to positions about 3,000 miles away.

This would mean that the British fleet would not have to sail 8,000 miles back to Britain, but could remain around British-owned Ascension Island off the western coast of Africa, where the United States, under a joint agreement with Britain, maintains an airfield.

The Argentines simultaneously would withdraw their army troops, unofficially estimated at about 10,000, from the Falklands to the Argentine mainland 300 miles away. Argentina invaded the islands and took control of them on April 2, and has steadily reinforced its occupation garrison.

The two countries would be required to withdraw half their forces within the first seven days and the remainder by 15 days.

Both Britain and Argentina have claimed sovereignty over the Falklands, whose English-speaking inhabitants have been under British control and administration for almost 150 years. Those inhabitants have always chosen to remain under British rule.

The new Argentine proposal reportedly does not directly address the sovereignty issue and does not even mention the word "sovereignty." But it does call for the Argentine flag to fly over the islands and would provide de facto Argentine sovereignty, in the view of some officials here.

The local administration of the Falklands would continue in the hands of the islanders, but the Argentines would control the police. The governor of the islands would be designated by Buenos Aires.

The pre-invasion legislative and executive councils on the island would be maintained, but the number of members would be expanded to include an equal number appointed by Argentina.

A transition period would be declared extending to December, 1982. A group composed of the United States, Britain and Argentina would be established to verify that the obligations of the agreement are carried out, and the United States would guarantee implementation.

Administration and diplomatic sources familiar with the Argentine proposal say that while it isn't much to go on, it probably is enough to have Haig go back to London and continue his role as a mediator in an effort to avoid a clash.

Sources suggested that Haig, knowing the British concerns from his previous trips, would also try and seek changes in the Argentine document that might improve its chances as a basis for negotiation.

The British fleet set sail for the Falklands on April 5, and it was widely believed and reported that the fleet would arrive in the region of the Falklands early next week. British officials privately gave similar estimates.

American sources now estimate, however, that the Royal Navy will not be near the Falklands until April 28 at the earliest, although the British could decide to get a few ships there earlier.

The fleet is said to be moving at about 12 to 15 knots. "If they were going any slower they'd be going backwards," said one informant. But he also added that the slow but deliberate speed also keeps up the psychological pressure on Argentina.

There are also what a number of officials called "rumors" that Washington has asked the British government to slow the pace of its armada to provide more time for negotiations. But these officials stress that this information is not confirmed.

Other sources say while the pace might have been slowed to give more time for a peaceful solution to be worked out, there are also other reasons for the long transit time. The British fleet, sources say, are using Ascension Island to rendezvous and pick up supplies and fuel. The slow pace allows that supply effort to be arranged most effectively. It may also allow time for some other ships that got under way later to join the task force.

Sources here say that the British, incensed over the island takeover, undoubtedly had to get their fleet under way fast as a sign of national determination. The fleet was probably not fully prepared, however, and so the additional time at sea is useful.