President Reagan launched another effort to increase political support for development of the MX missile today, arguing that critics have failed to understand his "dual approach" of seeking both to modernize U.S. nuclear weapons and to negotiate a reduction of superpower arsenals.

In a speech to 5,000 American Legion delegates here, Reagan said there has been "encouraging movement" in arms reduction negotiations with the Soviet Union, indicating this was evidence that his approach was working.

Saying his critics "willfully ignore" this "hand-in-hand" relationship of nuclear arms modernization and negotiations, the president argued that the "peace movement" would rather "wage peace by weakening the free." He suggested that it was making "the same old mistake" that British Prime Minister Neville Chamberlain did in seeking peace with Nazi Germany before World War II.

Reagan used his speech to the 65th annual convention of the American Legion to begin building support for House votes next month on appropriations for the MX long-range, multiple-warhead nuclear missile. He has been losing support for the MX among Democrats who voted for it previously but have since expressed doubts about Reagan's commitment to nuclear arms reductions.

The president was given a warm but not wildly enthusiastic reception by the Legionnaires. Outside the hall, several hundred demonstrators carried placards protesting his nuclear arms buildup and budget cuts for social programs. Some protested the assassination in Manila Sunday of Philippine opposition leader Benigno Aquino Jr.

Reagan, who is making a series of political speeches this week, also made a wide-ranging review of his foreign policy efforts that echoed his 1980 presidential campaign theme of "peace through strength."

On arms reductions, he noted that for the first time in the strategic arms reduction talks (START) negotiations, "the Soviets are willing to talk about actual reductions." He also said there has been "movement" on verification issues at the conventional force talks in Vienna, and "progress" in discussing confidence-building measures.

He said these indicators, while "modest," also "point in the same positive direction: new hope for arms reductions and a more secure world."

Reagan also attempted to answer those critics who say he has focused too heavily on the arms buildup. He said the administration has "steadfastly" pursued both a modernization of strategic forces and arms cuts.

"There is no contradiction in this dual approach, despite what some of the critics in Washington might have you believe," Reagan said. He added that the MX, as well as the effort to develop a new, small, single-warhead missile, will "maintain state-of-the-art readiness" against the Soviets but also provide an "essential incentive" for Moscow to negotiate seriously.

Accusing his critics of often missing this main point, Reagan said that "one argument contends that the MX Peacekeeper would pose a first-strike threat to the Soviet Union."

But this "runs counter to the whole history of America," he added. "Our country has never started a war, and we have never sought, nor will we ever develop, a strategic first-strike capability."

Reagan contended that "there is no way that the MX, even with the remaining Minuteman force, could knock out the entire Soviet ICBM force. So the argument is a false one, both philosophically and technically.

"What we really want . . . is enough force that tells the enemy we would do them a lot of damage," Reagan said in a comment that hadn't been included in his prepared text.

In discussing first-strike capability, Reagan did not mention the Navy's new Trident II missile, which is scheduled to be operational late in the 1980s, soon after the MX. The Trident II is advertised as being as accurate as the MX, and some arms control advocates argue that the combination of the MX and the Trident II will give the United States a first-strike capability when they are deployed.

Going beyond the MX, Reagan attacked the "so-called 'peace movement' " that has provided much of the opposition to the MX and his defense buildup.

"Neville Chamberlain thought of peace as a vague policy in the '30s, and the result brought us closer to World War II," Reagan declared. "Today's so-called 'peace movement'--for all its modern hype and theatrics--makes the same old mistake. They would wage peace by weakening the free. That just doesn't make sense.

"My heart is with those who march for peace," the president added. "I'd be at the head of the parade if I thought it would really serve the cause of peace." But he said the "real peace movement" is made up of people like the Legionnaires who "understand that peace must be built on strength."

On his broader foreign policy efforts, Reagan said "we have no intention of becoming policeman to the world." But he said the United States has a "responsibility to help our friends keep the peace."

Reagan defended his efforts to help friendly nations in Central America with a "security shield" of U.S. forces.

"Now there are some--in Moscow and Havana--who don't want to let our Caribbean neighbors solve their problems peacefully," he said. "They seek to impose their alien form of totalitarianism with bullets instead of ballots."

Reagan described the goals of his Central America policies as helping people of the region build "a better life--to help them toward liberty and to help them reverse centuries of poverty and inequity." He dropped from the prepared text the goal of helping them "toward peace."

He also attacked Col. Muammar Qaddafi of Libya for what he called "naked, external aggression" in helping rebels in Chad.

Reagan added that the Libyans are drawing upon $10 billion worth of Soviet arms and ammunition, including "Soviet-built fighter-bombers, T55 tanks and artillery in a blatant attempt to destroy a legitimate government."

"There's a democratic revolution going on in this world," he said. "It may not grab the headlines, but it's there and it's growing. The tide of history is with the forces of freedom--and so are we."