On the 20th anniversary of President Kennedy's successful call for a halt to testing atomic weapons in the atmosphere, an assortment of peace groups and members of Congress yesterday appealed to President Reagan and Soviet leaders to show the same kind of "political will" on further arms limitations.

At a news conference on Capitol Hill, a number of liberal congressmen, former government officials and representatives of some 40 peace and anti-nuclear groups were generally critical of Reagan administration nuclear arms and testing policies.

The groups urged support of resolutions in the House and Senate calling on Reagan to resume negotiations with the Soviets, which the White House suspended last July, on a comprehensive test ban treaty that would outlaw all nuclear tests, including scores of underground tests made each year by both countries.

The bills also urge Reagan to send to the Senate for consent the Threshold Test Ban Treaty of 1974 limiting the size of underground tests and the Peaceful Nuclear Explosion Treaty of 1976. Those pacts, signed by former Soviet President Leonid I. Brezhnev and by Presidents Nixon and Ford, respectively, have never been ratified by the United States.

The Reagan administration decided it had serious reservations about U.S. ability to verify Soviet compliance with such accords. The White House is also not convinced it can end underground testing and have confidence that U.S. weapons being developed will work.

Retired Rear Adm. Gene R. LaRocque, director of the Center for Defense Information and a critic of Pentagon policies, said that the administration wants to build some 17,000 new nuclear weapons in the next 10 years and that "the United States and the Soviet Union are on a course toward nuclear war. But if you can't test" those new weapons, confidence in their effectiveness and thus the likelihood of using them will recede, he said he believes.

Since the nuclear age began, some 1,415 atomic explosions have taken place, LaRoque said. Of these, 748 were by the United States, 492 by the Soviet Union, 113 by France, 35 by Britain (its were carried out by this country), 26 by China and one by India.

Since the limited test ban, the United States and Soviet Union, according to Rep. Edward J. Markey (D-Mass.), have conducted more than 650 underground tests. They continue at about one per week, LaRocque added, and the United States marked the anniversary of Kennedy's 1963 speech at American University by conducting another such test.

After hundreds of test explosions in the atmosphere in the early 1960s spread fear and some radioactivity worldwide, Kennedy proposed negotiations between the United States, Soviet Union and Britain to halt testing in the atmosphere, outer space and under water. Agreement was reached in 10 days. It was the first and one of the most important arms control agreements of the atomic age.

W. Averell Harriman, who Kennedy sent to Moscow to negotiate that treaty, sent word to the group here yesterday that "I can think of no better way to honor President Kennedy's initiative than to complete the task he began. The comprehensive test ban negotiations, too long suspended, should be resumed and brought to a successful conclusion."

The Carter administration came close to completing the comprehensive test ban negotiation in 1979 but the effort foundered after the Soviet invasion of Afghanistan and other pressures. Paul C. Warnke. director of the Arms Control and Disarmament Agency under Carter, told the news conference that an agreement could be completed next month if there was the willingness to do so.

Markey said that the "glimmer of hope" sparked by Kennedy's 1963 initiative "has largely been extinguished" by an administration which he said is more interested in an arms race rather than arms control.

Sen. Edward M. Kennedy (D-Mass.) sent a statement saying that "The promise we hear is arms control . . . , but the reality we see is MX missiles and continuing nuclear escalation."