President Reagan told Argentina's President Raul Alfonsin yesterday that "the communist tyranny imposed on Nicaragua" cannot be allowed to "spread to the free lands of the Americas," but Alfonsin replied that peace in Central America depends on dialogue and nonintervention.

In welcoming Alfonsin to the White House, Reagan again asked Congress to renew covert aid for rebels, known as "contras," fighting the leftist Sandinista government in Nicaragua. He charged again that the Sandinistas, who took power after the fall of Anastasio Somoza in 1979, had betrayed the Nicaraguan revolution.

"The Nicaraguan people are joining the ranks of the freedom fighters," Reagan said. "Nearly three times as many men are fighting the communists right now as the Sandinistas had fighting Somoza before they seized power."

His assertion about the size of the rebel forces marked a substantial jump from the figure he used in Quebec Monday at a luncheon given by Canadian Prime Minister Brian Mulroney. There, Reagan said, "More than twice as many people are fighting in the field right now against the Nicaraguan communist regime as fought against Somoza."

The gap between the two figures caused reporters at a White House briefing on the Alfonsin visit to inquire whether the contras' strength had grown so rapidly in less than 24 hours or was the product of Reagan's rhetorical zeal. U.S. officials at the briefing replied that they would try to provide a specific count later.

After yesterday's meeting, Reagan and Alfonsin issued a declaration expressing "their gratification and support for the spread and strengthening of democracy and individual freedom in the Western Hemisphere."

But Alfonsin, who took office last year after seven years of military dictatorship, joined other elected civilian presidents in Latin America and carefully avoided endorsing the U.S. emphasis on military solutions in Central America.

"I am convinced that it is through dialogue that we will be able to reach peace," Alfonsin said in Spanish. "And on the basis of the principle, the longstanding principle of international law in Latin America of nonintervention, that will give us the possibility of democracy and pluralism to succeed without extracontinental interventions . . . . "

The covert war against the Sandinistas was launched with substantial assistance from Argentine military advisers. However, after the United States sided with Britain against Argentina in the 1982 Falkland Islands war, Argentina began to disengage, and the Central Intelligence Agency took direct control of the contra movement until Congress ordered an end to U.S. funding last year.

Shortly after he became president, Alfonsin cut off the last Argentine aid to the contras. Since then, Argentina's policy toward Central America has been to support the "Contadora process" -- negotiations aimed at achieving a comprehensive solution to tensions in the region.

Argentina is struggling to repay a $48 billion foreign debt and to arrest an 800 percent annual inflation rate. Alfonsin, in his White House remarks, made clear his frustration at reconciling the fiscal austerity demanded by the International Monetary Fund with the hardships it imposes on his countrymen.

"We are making the necessary adjustments to overcome the obstacles of our economy," he said. "But we cannot make adjustments that will actually impose sacrifices on those who have less . . . . To ask from our peoples a bigger effort is to condemn them to marginality, to extreme poverty, to misery."