President Reagan, calling for "dismantling of the nuclear menace," today proposed reducing by one-third the strategic missile arsenals of the United States and the Soviet Union.

Speaking at the commencement ceremony of Eureka College, from which he was graduated 50 years ago, Reagan unveiled a two-phase plan of nuclear arms reductions and urged the Soviets to join in discussions on them by the end of June.

"I believe that the West can fashion a realistic, durable policy that will protect our interests and keep the peace, not just for this generation, but for your children and grandchildren," Reagan said to a burst of applause.

The first phase of the president's proposal would reduce ballistic missile warheads to "equal ceilings at least a third below current levels," with no more than half of these missiles based on land. This would cut the roughly equivalent level of warheads on both sides from 7,500 to 5,000. A prime goal is reduction of "the most destabilizing nuclear systems," a reference to the powerful and accurate Soviet SS18 and SS19 missiles.

A second phase, on which the president provided no details, looks to an equal ceiling on all strategic nuclear forces, with the apparent but unspecified goals of preventing either superpower from launching a successful first nuclear strike against the other.

"In both phases, we shall insist on verification procedures to ensure compliance with the agreement," Reagan said.

In Moscow, in an apparent attempt to take the edge off Reagan's arms control initiative, Defense Minister Dmitri F. Ustinov said in a sharply worded article in Pravda that "The Soviet Union will not allow the existing balance of forces to be disrupted."

Speaking to an audience of more than 2,000 packed into a sweltering, metal-roofed gymnasium, the president jokingly remarked that "it isn't true that I just came back to clean out my gym locker." Reagan wore the red robes of the honorary doctorate he received when he addressed the commencement class of 1957, 25 years after he graduated, and he quipped: "Mind if I try for the 75th?"

In his speech, Reagan said he was willing to negotiate in good faith on Soviet counterproposals. A senior administration official said today that he expects the Russians to counter with some proposal to reduce the number of bombers, in which the United States has a definite edge. The official said the United States is prepared to negotiate on this issue.

Reagan also hinted that he was willing to accept Soviet President Leonid I. Brezhnev's proposal for a fall summit meeting.

"I have already expressed my own desire to meet with President Brezhnev in New York next month," Reagan said. "If this cannot be done I would hope we could arrange a future meeting where positive results can be anticipated. And when we sit down, I will tell President Brezhnev that the United States is ready to build a new understanding based upon the principles I have outlined today."

Brezhnev, who is 75 and ailing, has rejected a June meeting, calling instead for a "well prepared summit" in October. Administration officials said last week that the president was prepared to accept such an offer, adding that Brezhnev's health appeared to be the main obstacle to such a meeting.

Until today, the 71-year-old Reagan has declined to make any reference to the health of the Soviet president. But in his speech to the Eureka graduating class Reagan made an oblique mention of Brezhnev's condition, saying that "both the current and the new Soviet leadership should realize that aggressive policies will meet a firm western response."

While Reagan was calling for "a new start toward a more peaceful, more secure world," he repeated many of his favorite accusations against the Soviet Union, which he referred to as "a huge empire ruled by an elite that holds all power and privilege" and fears that this power is slipping from its grasp.

"The Soviet empire is faltering because rigid, centralized control has destroyed incentives for innovation, efficiency and individual achievement," Reagan said. "Spiritually, there is a sense of malaise and resentment."

The president said that despite its social and economic problems, "the Soviet dictatorship has forged the largest armed force in the world." He repeated his longstanding view that a military balance is needed to counter this force but also said that the West would respond with expanded trade and other forms of cooperation if the Soviet Union embarked on peaceful policies.

Reagan called attention to the situation in Poland, where he said the Soviet Union has "refused to allow the people of Poland to decide their own fate, just as it refused to allow the people of Hungary to decide theirs in 1956 or the people of Czechoslovakia in 1968."

If martial law is lifted, political prisoners released and a dialogue restored with the Solidarity Union, Reagan said the United States was prepared to join in a program of economic support for Poland.

But the speech bristled with skepticism about Soviet intentions.

"Unfortunately, for some time suspicions have grown that the Soviet Union has not been living up to its obligations under existing arms control treaties," Reagan said. "There is conclusive evidence the Soviet Union has provided toxins to the Laotians and Vietnamese for use against defenseless villagers in Southeast Asia. And the Soviets themselves are employing chemical weapons on the freedom fighters in Afghanistan."

The timing of today's speech was dictated in part by the president's desire to demonstrate in advance of his European trip next month that he is serious about discussions with the Soviet Union that would lead to reduction of nuclear weapons and also to take the initiative on the arms control issue away from advocates of an immediate nuclear weapons "freeze" at present levels.

The president offered no prospect for quick or easy success.

"The monumental task of reducing and reshaping our strategic forces to enhance stability will take many years of concentrated effort," Reagan said. "But I believe that it will be possible to reduce the risk of war by removing the instabilities that now exist and by dismantling the nuclear menace."

Administration officials said they hope the discussions will proceed at a brisker pace than the negotiations that led to the SALT I treaty signed in 1972 or the SALT II treaty, which was withdrawn by President Carter in 1979 after it became clear that the Senate would not ratify it. The negotiations leading to that ultimately unsuccessful effort took seven years.

Reagan said that he had written to Brezhnev outlining his proposal and directed Secretary of State Alexander M. Haig Jr. to approach the Soviet government proposing initiation of the strategic arms reduction talks (START) "at the earliest opportunity."

"We will negotiate seriously, in good faith, and carefully consider all proposals made by the Soviet Union," Reagan said. "If they approach these negotiations in the same spirit, I am confident that together we can achieve an agreement of enduring value that reduces the number of nuclear weapons, halts the growth in strategic forces, and opens the way to even more far-reaching steps in the future."

Reagan's return to the small liberal arts college from which he graduated in 1932 was a sentimental occasion. He has come back to Eureka--as movie actor, governor of California and political candidate--many times since he left Illinois. During a speech at Eureka in October, 1980, Reagan referred to the years he had spent at the college as the happiest of his life.

Often, Reagan has said that those who share the memories of a small college enjoy a richer tradition than many graduates of larger, better-known universities.

"If it is true that tradition is the glue holding civilization together, then Eureka has made its contribution to that effort," Reagan said. "Yes, it is a small college in a small community; it is no impersonal, assembly-line diploma mill. As the years pass . . . you'll find the four years you have spent here living in your memory as a rich and important part of your life."

After his speech, Reagan went by helicopter to Peoria, where he attended a reunion of the Eureka class of '32, shaking hands with each of the 37 fellow alumnae who attended and their spouses. One former classmate, Karl Meyer, who roomed in the same fraternity house with Reagan, said he was "honest, poor, a helluva nice guy."