President Reagan appealed to the American people last night to support his request for increased military spending, saying that cuts in the defense budget would jeopardize arms control negotiations with the Soviet Union and "may put peace itself at risk."

In a nationally televised address from the Oval Office, Reagan argued that it would be "reckless, dangerous and wrong" to reduce the U.S. military budget in the face of the "enormous weapons investment" of the Soviets.

Administration advisers said they hoped Reagan's speech would help to change public perceptions that the United States is spending too much for defense, but congressional leaders of both parties predicted during the day that Congress would make reductions in the administration's defense budget requests.

The size of the defense budget is one of the most contentious issues between Congress and the administration in the struggle to meet deficit targets established by the Gramm-Rudman-Hollings balanced-budget law.

"Millions of Americans actually believe we are now superior to the Soviet Union in military power," Reagan said. "Well, I'm sorry, but if our country is going to have a useful debate on national security, we have to get beyond the drumbeat of propaganda and get the facts on the table."

Reagan said that the Soviets hold a numerical superiority in intercontinental ballistic missiles, tanks, combat aircraft, submarines and artillery.

"But it is not just the immense Soviet arsenal that puts us on our guard," Reagan said. "The record of Soviet behavior -- the long history of Soviet brutality toward those who are weaker -- reminds us that the only guarantee of peace and freedom is our military strength and our national will."

Reagan's speech illustrated the difficulty the administration is having in building a political consensus for additional military spending after five years of budget increases that the president said has brought the Soviets to the bargaining table in Geneva.

Last night the president pointed with pride to the military spending of the past five years but gave equal weight to what he called "the hard, cold reality of our defense deficit."

A senior administration official who briefed reporters before the speech was asked whether he thought the United States held a military edge over the Soviets, and responded, "It's a close call."

The defense budget for fiscal 1981, Reagan's first year in office, was $180 billion, about 24 percent of federal spending. Estimated defense spending for fiscal 1987 is $320 billion, about 28 percent of federal spending.

Reagan is seeking what he described as "a modest 3 percent" growth in the defense budget this year. He is calculating from a level preliminarily adopted by Congress last summer. Congress later approved additional cuts and then enacted the Gramm-Rudman-Hollings legislation calling for a balanced budget by fiscal 1991. If Reagan's budget request for fiscal 1987 is measured against actual spending for the current 1986 fiscal year, the increase for fiscal 1987 would be 8 percent above inflation.

During the last five years, public support for increased military spending has dropped from 72 to 22 percent, as measured by Washington Post-ABC News polls. An administration official said that White House polls showed a similar decline in public support for defense spending, partially because of concern about reports of Defense Department waste and inefficiency.

The president took issue with these criticisms last night, claiming "huge savings" in defense spending even while acknowledging that "getting control of the defense bureaucracy is no small task."

He said the "fraud and abuse" that had been widely publicized had been uncovered by the Pentagon and that Defense Secretary Caspar W. Weinberger "should be praised, not pilloried, for cleaning the skeletons out of the closet."

But Reagan also promised that "where defense reform is needed, we will pursue it" and took note that the commission he appointed to study defense management and procurement practices will be reporting on Friday. Administration officials said the proposals of this body, known as the Packard Commission, will be the subject of Reagan's radio speech Saturday.

In reviewing the record of the past five years, Reagan gave special emphasis to his missile defense proposal, the Strategic Defense Initiative (SDI), which he unveiled in another televised address on the defense budget three years ago.

Last night Reagan described the SDI as the program "that could one day free us all from the prison of nuclear terror," and said "it would be pure folly for the United States not to press forward with SDI when the Soviets have already invested up to 20 years on their own program."

Reagan claimed that the message of SDI, sometimes called "Star Wars," had influenced the Soviets to come to the bargaining table in Geneva and say that they accept the idea of reducing nuclear weapons. But the president made no predictions on whether an arms control agreement would be reached beyond saying, as he has in the past, that "if the Soviets truly want fair and verifiable agreements that reduce nuclear forces, we will have those agreements."

The president spent the first half of his speech praising the record of his administration in restoring American military strength and American spirit.

"The past five years have shown that American strength is once again a sheltering arm for freedom in a dangerous world," he said. "Strength is the most persuasive argument we have to convince our adversaries to negotiate seriously and to cease bullying other nations."

The president said that when he arrived in office, "guerrillas in El Salvador had launched what they called their 'final offensive' to make that nation the second communist state on the mainland of North America.

"Many people said the situation was hopeless; they refused to help," Reagan said. "We didn't agree; we did help. Today those guerrillas are in retreat. El Salvador is a democracy and freedom fighters are challenging communist regimes in Nicaragua, Afghanistan, Angola, Cambodia and Ethiopia."

After praising his administration's record on modernizing the armed forces, Reagan said that his defense program would be guided by four principles.

The first, he said, was that "we must be smart in what we build" and counter Soviet numerical advantages with sophisticated, high-technology weapons. Next, he said that U.S. security assistance for other nations must be maintained and increased because "our friends can perform many tasks more cheaply than we can."

The other principles, he said, were making necessary defense reforms, based on the commission report he will receive Friday, and reducing U.S. dependence on nuclear weapons through SDI and technology which "can provide us with the means not only to respond to full-scale aggression but to strike back at terrorists, without harming innocent civilians."

House Majority Leader James C. Wright Jr. (D-Tex.), delivering the Democratic response, accused the administration of "misplaced priorities" and said Reagan's request for more defense spending is tied directly to the threat he said is posed by the federal deficit.

"We have some very fundamental differences over spending priorities and the amount of debt we are willing to place upon the backs of our children," Wright said. "We think the deficits themselves pose a danger to our national security."

Wright said Congress has already enacted the largest peacetime buildup in military spending in history, a "force-feeding" that he said has produced Pentagon waste but little additional security.

Now, he said, Reagan wants still more for the military while attempting to cut federal assistance for education, health care, job training, law enforcement, environmental and other domestic programs.

"The American people know that real national security depends on certain other things equally as important to the country's future as armaments and weapons," he said. "It depends first of all on education -- the brainpower of our citizenry."

Earlier, House Minority Leader Robert H. Michel (R-Ill.) conceded that Reagan's defense spending increase "will be reduced," adding that the Republican role in Congress will be to "keep the reductions in bounds."

Michel said he favored a real increase in defense spending next year but would not say how much it should be. He also said that because of the pressure for deficit reduction, some House Republicans would be satisfied with "zero real growth" in military spending that kept pace with but did not exceed the inflation rate.

As Reagan spoke, lightly falling snow was clearly visible through the windows of the Oval Office. The camera frequently also showed pictures of the president's children and grandchildren.

"We've come so far together these last five years -- let's not falter now," Reagan said in concluding the 23-minute address.

"Let's maintain that crucial level of national strength, unity and purpose that has brought the Soviet Union to the negotiating table, and has given us this historic opportunity to achieve real reductions in nuclear weapons and a real chance at lasting peace. That would be the finest legacy we could leave behind -- for our children and their children."