President Reagan announced yesterday that the United States will begin strategic arms reduction talks with the Soviet Union on June 29 and he pledged to "refrain from actions which undercut" the unratified Carter-Brezhnev pact and other arms control agreements so long as the Soviets show the same restraint.

Speaking at Memorial Day ceremonies in Arlington National Cemetery, an emotionally stirred Reagan declared it a "fitting occasion" to announce the beginning of the START talks to reduce strategic nuclear weapons and to talk about his "quest for peace." He called for "treaties that can someday bring about a reduction in the terrible arms of destruction, arms that threaten us with a war even more terrible than those that have taken the lives of the Americans we honor today."

Reagan showed himself, however, to be unflinching in his long-held, hard-line view of the Soviets' system of government and their aspirations to global expansion.

He told the flag-waving crowd packed into the cemetery's Amphitheater under a sweltering sun: " . . . We must never fail to note, as frequently as necessary, the wide gulf between our codes of morality. . . . We must never hesitate to acknowledge the irrefutable difference between our view of man as master of the state and their view of man as servant of the state.

"It is this honesty of mind," he said, "that can open paths to peace, that can lead to fruitful negotiation."

For Reagan, whose administration has been marked by an emphasis on a massive buildup of arms, the twin announcements of the start of arms reduction talks and his intention to observe the limits of the SALT II treaty were clearly efforts to defuse the strong anti-nuclear movement in Europe and its swelling ranks in this country. Administration sources had indicated last week that he wanted to make the statement about abiding by existing nuclear arms control agreements before he leaves Wednesday for a nine-day trip to Europe where he is to participate in an economic summit at Versailles and a meeting of the North Atlantic Treaty Organization in Bonn.

While virtually all NATO countries would like to see the United States formally ratify the SALT II agreement negotiated by President Carter and Soviet President Leonid Brezhnev in 1979, Reagan administration officials have firmly ruled that out. They argue that that would formalize and legitimize the very large Soviet advantage in land-based missiles and would lessen the Soviets' incentives to negotiate arms reduction.

The announcement of the beginning of strategic arms reduction talks on June 29 in Geneva was made simultaneously in Washington and Moscow at 11 a.m. yesterday, timed to be disclosed just minutes before Reagan's speech. A one-paragraph joint statement by the two governments said, in part: "Both sides attach great importance to these negotiations." Ambassador Edward Rowny will head the U.S. delegation. His Soviet counterpart will be Ambassador V. P. Karpov.

Reagan had laid out his proposal for a dramatic reduction in Soviet and American nuclear missiles in a speech on May 9 in Illinois at his alma mater, Eureka College. Nine days later, in a speech in Moscow, Brezhnev signaled the readiness of his country to talk about reducing strategic nuclear arms, calling Reagan's proposals a "step in the right direction."

But Brezhnev criticized Reagan's plan as being "absolutely unilateral in nature" and he advocated a nuclear freeze, which is popular in Western Europe and among many anti-nuclear advocates in the United States but not in the White House.

An administration spokesman said diplomatic negotiations followed Brezhnev's remarks, culminating in the joint announcement yesterday. He said no arrangements have been made for a summit bringing together Reagan and Brezhnev. Both have expressed a willingness to come together for such a meeting but have engaged in prolonged intercontinental jousting over when and where.

During the presidential campaign, Reagan had called the SALT II agreement "fatally flawed" and used it as one of several examples of what he described as Carter administration policies that had so weakened U.S. defenses that war had become more likely.

The agreement has never been brought to the Senate floor for debate and a vote. Carter formally requested that action on it be deferred after the Soviet intervention in Afghanistan but even before then many in the Senate doubted whether the necessary two-thirds margin of support to get it ratified existed.

Although once in office the Reagan administration abided by the restraints of both SALT II and the initial five-year SALT I strategic arms agreement signed by the two superpowers during the Nixon administration in 1972, there has been bickering and conflicting public statements over whether they would continue to do so from within the administration.

The effect of Reagan's promise yesterday not to "undercut" strategic arms agreements "so long as the Soviet Union shows equal restraint" is to limit the land-based and submarine-based missile launchers in the Soviet and American nuclear arsenals and prohibit adding additional warheads to existing missiles. The agreements also rule out construction of new underground missile silos or deployment of mobile missiles, which could roam the countryside and perhaps escape detection by picture-taking satellites.

But Secretary of State Alexander M. Haig Jr. flatly rejected as "dead" any possibility of formal ratification of SALT II--a position that has drawn criticism from numerous influential public figures and lawmakers.

Former secretary of state Henry A. Kissinger said he had "great difficulty understanding why it is safe to adhere to a nonratified agreement while it is unsafe formally to ratify what one is already observing."

However, administration officials counter that by abiding by the limits of SALT II but not ratifying it, they are able to maintain interim restrictions on nuclear arms without endorsing the very large advantage the Soviets have in land-based missiles.

One of the primary aims of the Reagan administration in the new negotiations announced yesterday is to reduce or remove the big Soviet lead over the United States in very large land-based missiles. Of the roughly 2,400 Soviet missiles, 1,400 are land-based. This includes 308 of the huge SS18s, each of which carries 10 atomic warheads. The United States has nothing to match this weapon.