President Reagan today began a self-styled five-day "working holiday" with a visit to the Caribbean nation whose government has been most supportive of his regional policies.

Reagan, whose domestic economic policies have come under increasing criticism at home, arrived here to the warm praise of Prime Minister Edward Seaga. The Jamaican leader praised Reagan's Caribbean Basin initiative as opening "a new window of opportunity for hard-pressed Caribbean countries to create the new employment and improved standards of living which are essential to all democratic systems of government."

Seaga had reason to praise Reagan, whose free-market advocacies closely resemble his own.

While the Reagan administration has been cutting domestic social programs, it has been increasing economic aid to Jamaica. In addition, this island nation would benefit heavily from a key provision of the Caribbean Basin initiative, announced by Reagan in February, that would remove U.S. tariffs on most goods imported from the region.

"Jamaica is the best example of what the Caribbean Basin initiative can accomplish," Seaga told reporters after a private meeting with the president.

Seaga, who in February, 1981, became the first foreign leader to visit Reagan after his inauguration, said the administration provided timely assistance when the General Services Administration agreed to purchase 1.6 million tons of bauxite after Jamaican mining companies suddenly decided to cut production drastically.

"That would have crippled the Jamaican economy at a crucial time of our economic recovery," Seaga said.

Seaga's export-minded government has placed heavy emphasis on U.S. private development and tourism. During his first year in office, which coincided with Reagan's, the Jamaican prime minister has presided over an economy in which the inflation rate has fallen from 28 percent to less than 5 percent; the unemployment rate also has dropped.

This is in marked contrast to the success of the Reagan domestic economic program. In an interview today, Seaga acknowledged that the Reagan administration was facing a difficult period but said it was too early to judge the outcome of the president's economic program.

Reagan responded to Seaga's praise with some of his own.

"The progress that you are making here with your own program shows what can be done when people living in a democratic society are given the opportunity to work and to enjoy the fruits of their labor," Reagan said on his arrival in Kingston early this afternoon.

Reagan continued with this theme in responding to an effusive toast by Seaga at a state dinner, but expanded his remarks to include a denunciation of Cuban and Soviet activities in the Western Hemisphere, Marxist-Leninism, and "socialistic schemes aimed at changing the nature of man."

The president's remarks were warmly greeted by an audience dominated by members of Seaga's market-oriented government and island industrialists.

Earlier, after a series of meetings, the two governments issued a joint statement pledging mutual commitment to the Caribbean Basin initiative and general support for U.S. policies in El Salvador.

However, Seaga, meeting with reporters, expressed concern that a right-wing coalition in El Salvador might try to undo some of the reforms initiated by the government of Jose Napoleon Duarte. Such action would be a mistake, he warned.

A senior Reagan administration official said after the meeting that Reagan had expressed the view that the United States must make a "permanent, long-term commitment" to the region beyond the $350 million in financial aid he proposed in his Caribbean initiative.

Seaga said that the most important aspect of the initiative is the elimination of most tariffs, an act that he said would have the effect of "magnetizing the region" for business investment.

Among several gifts that Seaga presented to Reagan was a framed copy of a statement by President John Adams about U.S.-Caribbean relations.

"The commerce of the West India Islands is part of the American system of commerce," the second president of the United States wrote. "They can neither do without us nor we without them."