MOSCOW (AP) _ New York Gov. Mario Cuomo arrived in Moscow on Sunday to begin a week-long visit to the Soviet Union that he says involves peace and politics, but not the presidency.

Cuomo, accompanied by his wife Matilda, was greeted at Moscow's Sheremetyevo airport by Vasily Kazakov, deputy chairman of the Council of Ministers of the Russian Federation, the largest of the Soviet Union's 15 republics.

The New York Democrat was to meet Monday with Vitaly Vorotnikov, chairman of the Russian Federation's Council of Ministers and a member of the ruling Communist Party Politburo.

On Wednesday, he is scheduled to meet with Anatoly Dobrynin, former Soviet ambassador to the United States and a member of the Communist Party Central Committee. The governor's press secretary, Gary Fryer, said Dobrynin had requested the meetign.

Cuomo said he would talk about expanding trade and student exchange programs with the Soviets, but that the main purpose of his trip was to help improve relations between the superpowers.

''You can't be the governor of the state of New York, concerned as you should be about the lives of 18 million people, and not be concerned about how we manage our relationship with the U.S.S.R.'' Cuomo said. ''I do not need to be a candidate for the presidency to have an interest in these subjects.''

During the flight from New York, Cuomo said it was not possible to appeal to morality when dealing with the Soviets.

''That's not the way you deal with them. They don't respond to your idea of morality any more than we would respond to their idea of morality,'' said Cuomo. ''We have a different sense of human dignity, of morality, of what's right and wrong.''

The only answer, he said, is to be ''as civil as possible. But in the end, you negotiate from strength.''

''You can't expect them to change any more than you should expect us to change fundamentally,'' he added. ''We will always be dealing with an authoritarian regime and that means you will always have to be wary.''

The tough talk from Cuomo may have been a reaction to criticism that he might be ''soft'' on communism. The criticism was leveled after he welcomed a Soviet delegation to a conference in western New York in August.

The governor has complained that such criticism was unfair, given that he was supposed to be welcoming the Soviets to his state, not antagonizing them.

Cuomo, who announced Feb. 19 that he would not seek the 1988 Democratic presidential nomination, said before leaving the United States that the Soviets should be interested in his political thoughts because he is a Democrat.

On Friday, President Reagan, who is a Republican, announced that he had reached an ''agreement in principle'' with the Soviets to ban superpower medium- and shorter-range nuclear missiles.

Reagan also said he would meet with Soviet leader Mikhail S. Gorbachev for a fall summit in the United States.

''I get the feeling that they are concentrating on President Reagan, as they must,'' Cuomo said of the Soviet leadership, speaking earlier this month in an interview.

But he noted that any arms agreement has to be ratified by the Senate, which the Democrats control.