President Reagan responded yesterday to the death of Leonid I. Brezhnev by calling for improved relations with the Soviet Union but turned down a proposal by his foreign policy advisers that he take what one of them called "the dramatic step" of attending the funeral of the Soviet president.

Reagan, rejecting the recommendation of Secretary of State George P. Shultz, said that Vice President Bush would head the U.S. delegation to Moscow.

Shultz had proposed that Reagan take the precedent-setting step of attending the funeral himself in an effort to improve U.S.-Soviet relations during a time of transition. "Our two nations bear a tremendous responsibility for peace in a dangerous time -- a responsibility that we don't take lightly," Reagan said in a statement opening his news conference last night.

However, he emphasized -- as he has many times in the past -- that he believes peace can be built only on a foundation of military strength.

After reconfirming his commitment to continued negotiations with the Soviets to reduce both nuclear and conventional forces, the president said: "But we shouldn't delude ourselves. Peace is a product of strength, not of weakness -- of facing reality and not believing in false hopes."

When Reagan was asked whether he would take any initiatives to reduce tensions between East and West, he responded that "it takes two to tango" and that he had already taken the first steps. The only example that he gave was the lifting of the grain embargo early in his administration. In deciding to send Bush to Brezhnev's funeral on Monday, administration officials disclosed, Reagan sided with top members of his White House staff against the recommendation of Shultz and other key foreign policy and national security advisers.

The Shultz recommendation was strongly opposed by White House chief of staff James A. Baker III and deputy chief of staff Michael K. Deaver, according to administration sources.

These sources said that national security adviser William P. Clark, who was described by others as a "broker" in the discussion, backed Shultz, as did Central Intelligence Agency Director William J. Casey. Those who advocated that Reagan travel to Moscow argued that it would signal his commitment to arms control and to improving strained U.S.-Soviet relations.

However, Secretary of Defense Caspar W. Weinberger and U.N. Ambassador Jeane J. Kirkpatrick, who have taken a hard line against the Soviets, were described as agreeing with the White House staff that Reagan should not go.

"It was a philosophic thing," said one administration official. "If there's progress made in Vienna and Geneva in troop reduction and nuclear arms control negotiations , the president would like to visit the Soviet Union. But there's been no opening, no sign of restraint from the Russians."

Some sources said the trip also would have been grueling for the 71-year-old Reagan, who is to travel to Chicago on Saturday for a tribute to his late father-in-law, neurosurgeon Loyal Davis.

Reagan did not go into any of these reasons at his news conference. Instead, he cited scheduling conflicts, including forthcoming visits by heads of state, an apparent reference to upcoming meetings with Israeli Prime Minister Menachem Begin.

The president added that he thought it was possible to continue the "search for peace" without "my attendance at the services."

Bush is currently on a seven-nation trip to Africa, which he would interrupt to attend the Brezhnev services. One official said it would be "convenient for the vice president to attend, since he is already abroad."

While the view inside the White House is that relations with the Soviets will remain basically unchanged in the wake of Brezhnev's death, Reagan tried yesterday publicly to sound a note of optimism about the prospects for arms reductions.

He began the day by sending a letter of condolence to Vasiliy Kuznetsov, first deputy chairman of the Presidium of the Supreme Soviet. The letter referred to Brezhnev as "one of the world's most important figures for two decades."

"I would also like to convey through you to the Soviet government and people the strong desire of the United States to work toward an improved relationship with the Soviet Union," his letter continued. "I look forward to conducting relations with the new leadership in the Soviet Union with the aim of expanding the areas where our two nations can cooperate to mutual advantage."

The president had been prepared for Brezhnev's death. He had been briefed Wednesday afternoon on the possibility that the Soviet leader had died. Clark called him at 3:35 a.m. yesterday to inform him that Brezhnev was dead.

Despite the peaceful tone of the initial White House statements yesterday, Reagan soon made clear that he was not wavering in his basic view that strength is the message the Russians understand most clearly.

In a Veterans Day observance at the White House, where Reagan awarded the Presidential Citizens Medal to World War II veteran Raymond Weeks, the president reiterated his oft-stated belief that it is military deterrence, more than anything else, that preserves world peace.

"Today, in this era of much more dangerous weapons, it is even more important to remember that vigilance, not complacency, is the key to peace," Reagan said. "This administration is committed to rebuilding our national defenses, which were permitted to erode during the last decade. We are now in the initial phases of that rebuilding, and we must continue to press forward in the years to come if we are to maintain a credible deterrent.

"But let the world understand our purpose is not belligerency but respect, not conflict but deterrence, and not war but peace. None of the wars that I have mentioned, or others before them, ever came about because this country was too strong. We shall never flag in our pursuit of a more peaceful world."

In his speech the president also quoted from John F. Kennedy's 1940 book, "Why England Slept," saying that among the reasons for England's failure to rearm before World War II "probably the most important was a firm and widely held conviction that armaments were one of the primary causes of war."

Administration sources said that the delegation tentatively scheduled to go to Brezhnev's funeral will include, in addition to Bush and Shultz, Senate Majority Leader Howard H. Baker Jr. (R-Tenn.) and House Speaker Thomas P. (Tip) O'Neill Jr. (D-Mass.) plus U.S. Ambassador to Moscow Arthur A. Hartman and some former U.S. secretaries of state, including Alexander M. Haig Jr.

A proposal to send former presidents Nixon, Ford and Carter, was rejected, according to sources. Nixon reportedly was told that if he wished to attend, he should go as a private citizen, and not as part of the official delegation.