Soviet leader Yuri Andropov appealed directly to the American people today by publicizing a letter he had written to an American girl assuring her that Russians want to live in peace with Americans and to trade and cooperate with them.

In a novel twist in Moscow's public diplomacy, Andropov's letter to Samantha Smith, a fifth-grader from Manchester, Maine, was distributed by the government news agency Tass.

The Soviet leader said he was replying to the girl's letter, which was among "many others" he had received since becoming general secretary of the Soviet Communist Party last November.

According to Andropov's letter, Samantha had asked him whether the Soviet Union and the United States could do something to prevent a nuclear war, and, "Why do you want to conquer the world or at least the United States?"

In his reply, Andropov said, "We in the Soviet Union are endeavoring and doing everything so that there will be no war between our two countries, so that there will be no war at all on earth."

Andropov recalled that the Soviet Union was devastated during World War II "in which we were allies with the United States" and that today the Russians want "very much to live in peace, to trade and to cooperate" with all countries "and certainly with such a great country as the United States."

Responding to her second question, Andropov said, "Nobody in our vast and beautiful country . . . wants war, be it big or 'small.' We want peace. We have a lot to do--grow grain, build, invent, write books and make space flights. We want peace for ourselves and for all people of the planet . . ."