Greece's Socialist government intends to use international cultural exchanges and domestic subsidies for art to reshape the way Greeks and the rest of the world see that country's recent history, according to Culture Minister Melina Mercouri.

"People abroad know about the ancient Greeks and the shipowners, and nothing in between," said Mercouri, the internationally known actress who is now minister of culture, "even though Greek poets have won two Nobel prizes in recent years. We must show the truth to them and to the Greeks themselves. In that way, exchanges and exhibitions become profound political acts."

Asserting that "400 years of Turkish occupation and then two centuries of foreign domination" had led to a significant suppression of artistic and intellectual life in Greece, Mercouri agreed with a reporter's characterization of her program as an attempt to launch "a cultural liberation movement" in Greece.

In an interview yesterday in New York, where she presided over the closing of the American tour of an exhibition of archeological finds from the time of Alexander the Great, Mercouri carefully dissociated herself from attacks raised by other European leftists against "American cultural imperalism." Such sentiments have been voiced principally by French Culture Minister Jack Lang at a recent UNESCO meeting in Mexico City.

But Mercouri emphasized that next year she hoped to triple state subsidies for Greek movie productions for theater and television release, in part to keep those markets from being flooded by "inferior soap-opera series and films. We must protect our own industry. We must provide funding for a national Greek cinema, while continuing to import what is good in American film."

Prime Minister Andreas Papandreou appointed Mercouri a year ago after his Panhellenic Socialist Party defeated the center-right politicians who had come to power in 1974. She said that being in politics resembles film-making more than she had imagined.

"There's always the surprise in the cutting room, where somebody else is in charge of editing," Mercouri said as she sipped a cup of black coffee and smoked Greek cigarettes in a hotel on Central Park South. "Now Andreas Papandreou is the great cutter . . . . So far we are still in the prologue of this political film, of his dream and his hopes for Greece."

Europe faces "not an American imperialism -- that is such a cliche -- but an invasion of American culture. It is very normal, because America has a great culture, and America influences, from blue jeans to rock-and-roll music. But we must protect our own product and artistic industries, too."

Greece has been reluctant in the past to participate in international cultural exchanges, in part because of sensitivity over the loss of the Elgin marbles to Britain.

But as the Alexander the Great exhibition was coming to an end last week in New York, a new exhibition -- featuring centuries-old Greek art works that are scattered in museums and private collections all across Europe -- was opening in Brussels. Cofinanced by Greece and Belgium, the exhibition will move to Athens later this year, and Greeks will have a chance to see works that are much better known abroad.

"The cultural exchange is a political act. The more you know of another country's historical and cultural life, the less you will be willing to destroy or distort. And Greeks must be shown their history, a history that was neglected by all these rightist governments," Mercouri said.

"I am not a fanatic on this," Mercouri asserted. "But Greeks have seen themselves through foreign eyes for too long. Because these rightist governments depended on foreign support, they encourged Greeks to accept an imitation culture, copied from France, Italy, Bavaria, from all over, and then from America."

Mercouri, 57, who was elected to the National Assembly last year from Piraeus, the Athens port district that was the locale of her best known film, "Never on Sunday," said that she has been a particular target of attack for Greek conservative parties "because they don't believe that an actress can do something serious. But I want to help bring what I know about culture and art into the government . . . . I just hope that President Reagan also remembers that he was an actor, and that he was a union leader."