Argentine warships were reported today to have left their home port for the South Atlantic, and U.S. Secretary of State Alexander M. Haig Jr. arrived here tonight amid indications that time for mediation in the dispute over the Falkland Islands was quickly slipping away.

On arriving at the airport here, Haig said "the task will not be easy" in reaching an accord between Argentina and Britain, "but the stakes are so great that they demand the ultimate effort of all participants in these discussions."

"A solution will require a flexible approach by both sides," Haig said, "not an abandonment of principles, but an important degree of defensible flexibility."

With approximately five days remaining before a British fleet is expected to reach the war zone marked by both Argentina and Britain in the South Atlantic, the Argentine state news agency Telam reported that Argentine warships had sailed from the naval base of Puerto Belgrano, about 300 miles south of Buenos Aires, early this afternoon.

The report, which cited unnamed sources, did not disclose how many of Argentina's 17 major naval ships had left port nor where they had gone, although reports by private Argentine news agencies said that the ships carried provisions for 20 days and included Argentina's rebuilt British aircraft carrier, the 25th of May.

The fleet movement from Puerto Belgrano would not have placed it in immediate danger of attack from British nuclear submarines patrolling the 200-mile area around the Falklands, since the naval base is about 930 miles north of the islands.

In Washington, the White House said that Argentine President Leopoldo Galtieri called President Reagan this afternoon and that the two held a 30-minute conversation on the situation in the South Atlantic. Reagan was said to have told the Argentine leader that a conflict in the hemisphere between two Western nations would be a tragedy that would leave a bitter legacy. The United States has treaty relationships with both countries.

The White House said Reagan had asked for restraint by both countries in the days ahead. Galtieri was said to have reaffirmed his personal desire for a peaceful resolution of the dispute.

British Prime Minister Margaret Thatcher went to the Defense Ministry in London Thursday for a briefing on British and Argentine military preparations, Washington Post correspondent Leonard Downie Jr. reported.

Thatcher and the three senior Cabinet members in her crisis management team were told that a few Argentine warships may have moved out of port, although apparently not toward the 200-mile zone around the Falklands in which Britain has threatened to sink them with hunter-killer submarines. Expressing doubts about Argentine claims that the zone had been penetrated by two small motor torpedo boats, a Defense Ministry statement said some Argentine ships "may, however, sail close to the Argentine mainland and even skirt the maritime exclusion zone in an attempt to score some propaganda advantage and bolster up morale in Argentina."

Thatcher and her aides--Foreign Secretary Francis Pym, Defense Secretary John Nott and Home Secretary William Whitelaw--also reviewed the progress of the steadily growing British naval task force dispatched to the South Atlantic. Responding to rumors that it may have slowed down while Haig negotiated, Thatcher said that the fleet was still steaming south at "full speed."

As preparations for a possible military conflict with the British fleet escalated around Argentina, widespread reports today also said that Argentina's armed forces had moved troops and heavy artillery to reinforce defenses on the island of South Georgia, some 900 miles east of the Falkland Island chain.

The icy, nearly barren South Georgia islands, which were seized by Argentine forces one day after their April 2 invasion of the Falklands, have been considered a possible first target for British forces in an armed conflict.

With Haig flying into Buenos Aires for the second time carrying "new ideas" in hisshuttle diplomacy mission between Argentina and Britain, Argentine officials continued to express hope that a formula for defusing the conflict with Britain could be found.

Haig and a delegation of U.S. officials talked with Galtieri and Foreign Minister Nicanor Costa Mendez for 10 hours last Saturday before flying to London with what were called suggestions by the Argentines for an agreement. The talks stalled on Monday while Haig was in London, apparently over such issues as the composition of a temporary administration of the islands and Argentina's demand to maintain its claim of sovereignty over the territory while negotiations continue.