Washington — As the presidential campaign begins in earnest, it becomes clear that the ''war-peace'' issue will be a key factor. President Reagan and Democratic challenger Walter F. Mondale focused this week on national defense and concerns about nuclear war in speeches before military veterans. Vice-President George Bush accused Democrats of wanting to ''give away the store'' on arms control and cut the Pentagon budget. Mr. Mondale's running mate, Rep. Geraldine A. Ferraro (D) of New York, asked rhetorically if Mr. Reagan in a second term would ''heighten the risk of war.''
Speaking to the American Legion Convention in Salt Lake City Wednesday, Mondale said Reagan had ''failed a crucial test of presidential leadership'' in not negotiating an arms control agreement with the Soviet Union.
A study of public attitudes and perceptions, scheduled to be released today, confirms why the campaign may turn on the war-peace issue.
The Public Agenda Foundation (in collaboration with the Center for Foreign Policy Development at Brown University) reports that Americans ''fear that we may be drifting toward a disaster that no one will be able to prevent.''
''So deep is the concern about the nuclear arms race that if the country does not have a method for considering our options in a calm, mature fashion, the concern of citizens could erupt in overreaction, overanxiousness, and support for action for its own sake,'' the report warns.
This study, which was directed by public-opinion analyst Daniel Yankelovich and funded by the Ford Foundation, indicates that most people believe the subject is too important to be left ''to the President and the experts.'' But it also shows ''murky areas of misinformation and inconsistency'' that could make it difficult for the candidates - especially Mondale and Representative Ferraro - to focus their criticism.
Hardly any Americans, for example, realize that it is US policy to use nuclear weapons first in some circumstances (such as Western Europe's being overrun by Warsaw Pact conventional forces). While 83 percent of those polled feel that ''there are limits to American power and that we can't be the policemen of the world,'' a majority also believe that ''whenever there is trouble in the world ... the chances are the Soviets are behind it.''
According to former National Organization for Women president Eleanor Smeal, the ''gender gap'' (showing women less supportive of Reagan than men) stands at about 10 percent, but a larger 20 percent on such things as the deployment of US troops overseas.
Among both men and women, an August Gallup poll showed most (47 to 35 percent) believing Mondale could do a better job of avoiding war. At the same time, however, half of those surveyed believed that Reagan could handle foreign relations better, compared with 33 percent for Mondale, and 48 percent agreed that Reagan is better able to deal with the Soviet Union, as opposed to 34 percent for Mondale.
Peace activists say Mondale will have to continue pressing the war-peace issue if he is to overcome Reagan's personal popularity, and they vow to help him do that. The number and strength of politically active peace groups has grown considerably in just two years. For example, the budget and membership of the antinuclear group SANE have tripled since 1982: The budget grew from $50,000 to $150,000 and membership grew from 30,000 to more than 100,000.
SANE, Freeze Voter '84, and the Boston-based Council for a Livable World are focusing their considerable fund-raising and get-out-the-vote efforts on key House and Senate races as well as on the contest for the White House. The nuclear-freeze movement will officially endorse the Mondale-Ferraro team today.
Even though nuclear-freeze groups support the Democratic ticket, the issue may have become too diffuse to make a difference. According to a Los Angeles Times survey covering 95 percent of the delegates to the Republican National Convention, 62 percent of them favor a freeze on the testing, production, and deployment of nuclear weapons, although Reagan opposes it.
Antinuclear and peace groups are supporting Democratic candidates almost without exception (Sen. Mark Hatfield (R) of Oregon is one). But they are not particularly hopeful that the Mondale campaign is ready to capitalize on an issue of major public concern.
''A lot of things are going to have to fall into place, and Mondale's going to have to run a virtually flawless campaign,'' says Mike Mawby, political director of SANE PAC.
''To date, it (the Mondale campaign) has not distinguished itself in terms of substance,'' says William Curry, executive director of Freeze Voter '84. ''That has to change.''