New York Gov. Mario M. Cuomo (D) said here last night that the United States should "seize this moment" when change is occurring in the Soviet Union to "try to begin to negotiate the end of the cold war."

Cuomo, who spent seven days in Moscow and Leningrad last month, spoke to 200 members of the foreign policy and political establishment in a Washington meeting of the Council on Foreign Relations. His speech -- but not the off-the-cuff remarks that followed -- was made public by the council.

Cuomo said the nearly completed treaty to eliminate U.S. and Soviet medium-range and shorter-range nuclear missiles is "a strong beginning, but it is only a beginning" of a broader military settlement. Because of a perceived need to replace missiles with conventional forces, he said, the missile treaty could actually add to U.S. military costs if it is not followed by other pacts.

He said other steps that are needed include "a substantial reduction in strategic {long-range} nuclear weapons {of} at least the 50 percent already mentioned {in U.S.-Soviet talks}; movement toward reducing and equalizing conventional forces; progress toward a comprehensive test ban {and} a ban on chemical weapons."

Cuomo added that "political issues must be dealt with as well, including Soviet withdrawal from Afghanistan and the need for substantial progress on the refuseniks and other human rights issues."

Recent U.S.-Soviet negotiations have covered all these areas.

Cuomo said that while "an age of ice will not be melted overnight," he said he believes there is perhaps the best opportunity in 40 years "to break out of the grip of the cold war and move gradually and surely toward greater mutual security and cooperation."

The governor said he found in the Soviet Union an economy that is "weak and growing weaker" and a people who are showing "the beginnings of restiveness" about their political and economic system.

"Soviet leaders are faced with a dangerous dilemma and they know it," he said. "They need to give their people more freedom in order to make progress, but if they give too much freedom they risk losing power."

Consequently, Cuomo said, the Soviet leadership "is walking a tightrope over a dangerous psychological and political abyss. It makes them vulnerable and -- it seems to me -- helps explain their disposition in recent negotiations."

Cuomo, who took himself out of the race for the 1988 Democratic presidential nomination on Feb. 19, has consistently declared he will not reconsider that position. He ended his address with a call for strong presidential leadership "to guide the nation through the turbulent political currents of this time."

Cuomo called on the presidential aspirants to discuss "the new and dramatic sounds coming out of the Soviet Union.