U.S. Secretary of State Alexander M. Haig Jr. and Argentine officials exchanged written proposals for resolving the dispute between Argentina and Britain over the Falkland Islands today during more than six hours of talks that left officials on both sides cautiously optimistic about a diplomatic solution to the crisis.

Haig, who arrived here last night in the fourth stopover of the U.S. mediation effort in London and Buenos Aires, met briefly with President Leopoldo Galtieri at the presidential palace this morning before beginning sessions with Foreign Minister Nicanor Costa Mendez.

As the talks at the Foreign Ministry broke near 8 p.m., Haig returned to his hotel while Costa Mendez went to the presidential palace to meet with Galtieri and the two other members of Argentina's ruling military junta. Costa Mendez later traveled alone to Haig's hotel room for more talks, officials said.

He left shortly after midnight, The Associated Press reported.

Officials said tonight that the talks were likely to continue Saturday and said it had not been determined when the U.S. delegation would leave Buenos Aires or whether it would go to London or return to Washington.

Both Argentina and the United States submitted written proposals for a solution to the two-week-old crisis during the talks here, sources said. Although officials of both countries refused to publicly characterize the discussions, one source said the U.S. delegation was in high spirits as it returned late tonight to a dinner of beef steak and shrimp.

Haig was joined at the Foreign Ministry today by Assistant Secretary of State for Inter-American Affairs Thomas O. Enders and special ambassador Vernon Walters as well as political and economic counselors.

Twice during the day the talks were adjourned while Argentine and U.S. officials conferred separately, officials said.

An Argentine presidential spokesman said Haig delivered a note to Galtieri from President Reagan following up on the telephone conversation between the two leaders last night and that the 35-minute morning meeting had been "frank and useful." Officials said the Foreign Ministry meetings were attended by economic and political specialists from both sides, indicating that the talks had reached the point of detailed negotiations.

Officials indicated that Haig's second round of talks here focused on a temporary formula that would eliminate the immediate risk of a military confrontation by mandating the recall of the British fleet and the 10,000 Argentine troops reported to be on the island, while leaving unresolved or vaguely treating the underlying issues of sovereignty and the islands' future government.

Meanwhile, there were reports here that three British journalists had been arrested in the Argentine town of Rio Grande last night after they were found taking pictures of an Argentine Navy air base.

The reports, which were not immediately confirmed by officials here, said that Simon Winchester of the London Sunday Times, and Ian Mather and Tony Prine of the London Observer had been charged with espionage and transported to the town of Ushuaia at the tip of Argentina's Tierra del Fuego, where they were placed under the jurisdiction of a federal judge.

The three journalists were reported missing by their newspapers earlier today. They had left Buenos Aires Sunday and had not been heard from since.

Even as a British armada sailed for the Falklands, high-level Argentine officials were upbeat about the possibility of reaching an agreement. Costa Mendez declared on television last night: "I am persuaded that Haig will not go off with his hands empty from this new visit to Argentina."

Argentina invaded the islands, which it calls the Malvinas, April 2 after 15 years of what Argentina says were fruitless negotiations over its claims that Britain had occupied the territory unjustly since 1833.

Argentine officials today gave no indication of the whereabouts of Argentina's naval fleet, at least part of which was reported yesterday to have left its port. But there was no indication that the warships, which have been quartered about 900 miles from the Falklands, were nearing the blockade zone around the Falklands where Britain has threatened to sink all Argentine ships.

Diplomatic sources here said that Britain was receiving information on the position of the Argentine fleet through use of a satellite to which NATO members have access.

The sources said, however, that the satellite's trajectory did not make possible clear pictures of Argentine activity on or near the islands themselves.

Diplomatic sources also said that despite reports that British warships might reach Argentine waters as early as next Tuesday, the fleet had left the island of Ascension only within the last day and was moving slowly. These officials said that the fleet was traveling at a speed of only about 12 knots when it left Ascension, at which rate it would not cover the 3,500 miles to the Falklands for about nine more days.

Argentina tonight submitted a new statement to the U.N. Security Council protesting what it says is Britain's extension of the blockade around the Falklands to include the air space over the islands.

The statement, released here by the Foreign Ministry, said that Britain had informed international civil aviation authorities that the air space above the Falklands was a zone of emergency and called the move "grave."

Argentina has been supplying its troops on the Falklands with a daily airlift from the southern port of Commodoro Rivadavia.