The White House said yesterday that it is still President Reagan's "sincere hope" that Soviet President Leonid I. Brezhnev will join him for an informal meeting on nuclear disarmament in New York in June but that Reagan will "study . . . carefully" Brezhnev's call for a "well-prepared" fall summit in Europe.

At the same time yesterday, Reagan, in the third of his Saturday radio addresses, condemned the Soviet Union for engaging "in the most massive arms buildup in history," invading Afghanistan and acting to "crush a spontaneous workers' movement in Poland."

"Let's not fool ourselves," he said in the five-minute, midday radio address to the nation. "The Soviet Union will not come to any conference table bearing gifts. Soviet negotiators will not make unilateral concessions. To achieve parity, we must make it plain that we have the will to achieve parity by our own effort."

White House spokesmen said that Reagan was informed, shortly before he went on the air, of news accounts from Moscow on the new Brezhnev offer. But they said the president chose not to alter his speech, which by coincidence was devoted to arms control issues and an attempt to defuse criticism from the growing nuclear arms freeze movement.

The spokesmen said national security adviser William P. Clark briefed Reagan on Brezhnev's proposal after the speech.

Later in the afternoon, presidential spokesmen issued a statement saying the White House did not interpret Brezhnev's remarks as a rejection of the informal invitation Reagan extended two weeks ago for a New York meeting in June when Reagan is scheduled to speak on nuclear disarmament at the United Nations.

In saying the president would study Brezhnev's proposal, White House spokesmen again warned that there must be a "reasonable chance" that a formal summit "would have worthwhile, positive results" before the United States agrees to one.

Reagan, in his radio address from Camp David, sought to defend his arms buildup against the budding movement advocating a nuclear weapons freeze.

Ground Zero, a Washington-based group describing itself as a nationwide project committed to educating the American public on nuclear war, plans to begin today a week of informational activities in 150 cities and 500 smaller towns, on 350 college campuses and in 1,000 secondary schools throughout the nation.

The administration has moved forcefully to counter the idea of a nuclear freeze. The State Department has published an eight-page "essay" entitled "The Nuclear Freeze" specifically for that purpose.

The essay argues, as Reagan has contended repeatedly, that the Soviets have a nuclear arms margin of superiority over the United States. That view is disputed by many experts.

In his radio address, Reagan said he did not disagree with the ultimate goal sought by advocates of a freeze, only their means for achieving it.

"I know there are a great many people who are pointing to the unimaginable horror of nuclear war," he said. "I welcome that concern. Those who've governed America throughout the nuclear age and we who govern it today have had to recognize that a nuclear war cannot be won and must never be fought.

"So, to those who protest against nuclear war, I can only say I'm with you."

Reagan said the way to "end this threat of doomsday which hangs over the world" is for the United States and Soviet Union to negotiate a nuclear arms reduction, which he said the Soviets have rejected "countless times" since World War II.

He said the administration is preparing a new proposal for reducing strategic nuclear forces and noted that the United States is already negotiating in Geneva on intermediate-range missiles targeted on Europe.

"We'll make every effort to reach an agreement that will reduce the possibility of nuclear war," he said. " . . . Perhaps one day we can achieve a relationship with the Soviet Union which doesn't depend upon nuclear deterrents to secure Soviet restraint."

In a Democratic response aired on radio two hours after Reagan's speech, Rep. Toby Moffett (Conn.) said the president's talk was not about arms control.

"It was a discussion of our enemy, the Soviet Union. We Democrats agree with him on Afghanistan and Poland, but we don't agree the Soviet Union is 10 feet tall. We don't believe they are stronger than America. And it serves no useful purpose for a president to keep suggesting they are," Moffett said.

"The sad fact, the sad truth, is that after 16 months in office, this president does not have a proposal" for reducing arms, Moffett said. "He has not articulated our interests, how we are threatened and what he is going to do about it."

The White House did not announce the topic of Reagan's speech this week until shortly before it was broadcast, apparently hoping to keep the Democrats in the dark.

Moffett's broadcast had been scheduled an hour after the president's speech, presumably not enough time for him to prepare a substantive response. But, as it turned out, Moffett's turn was postponed one hour, giving the Democrats extra time.

Moffett was delayed because his wife, Myra, was at Georgetown Hospital giving birth to their first child, a girl.