The Defense Department, after pledging not to involve itself in the presidential campaign, devised an election-season "public affairs plan" late in the summer designed to win "public understanding and support" for the administration's management of military programs, according to memos released yesterday.

The plan, which covers the period from Sept. 5 through Nov. 3, calls for speeches by Defense Secretary Caspar W. Weinberger and his deputy, an "active letter-to-the-editor program" and the enlistment of military commanders at bases around the country in selling the administration's position. It also emphasizes the public relations benefits of productivity awards to Defense Department employes.

Michael I. Burch, assistant secretary of defense for public affairs, yesterday said that the eight-week public affairs campaign is not related to the presidential election on Nov. 6 and that similar efforts will continue after that date.

Burch said the plan is a legitimate response to increasing criticism of the Pentagon's management of weapons procurement, criticism that he said does not give the Defense Department credit for reforms that have begun to work.

"I don't think it's political at all," he said. "This plan or initiative does end in November, but it's a theme we've been promoting for 3 1/2 years."

Burch said several times during the spring and summer that Weinberger and the Pentagon would stay out of the political campaign.

One memo, obtained and released by Common Cause, shows that at least some top officials in the Pentagon were concerned about the impact on the political campaign of "horror stories" about spare parts prices and other matters. The July 24 memo, from Russell A. Rourke, the Defense Department's congressional liaison, notes that three Republican senators were worried about recent stories about the Pentagon scrapping valuable, unused equipment.

"This, coupled with the press we received on prices paid for selected spare parts, i.e., claw hammer, stool cap, allen wrench, if gone unchecked, will definitely be a key campaign issue," Rourke wrote to the under secretary of defense, urging efforts to counter the reports. "The opposition will cite these examples and portray the department as having serious management problems."

Questions about Pentagon procurement have increased as the military budget has risen to record peacetime levels in the past three years. The public affairs plan, which Weinberger approved, was designed to quell some of that criticism, officials said.

Fred Wertheimer, president of Common Cause, wrote to several congressional committees yesterday asking them to investigate "possible improper political involvement by DOD Department of Defense officials during the 1984 national election campaigns." Wertheimer said that some of the public relations efforts "undermine the nonpartisan nature of the Pentagon's national defense responsibilities" and may violate the Hatch Act, which limits the political activities of government workers.

The plan is detailed in an Aug. 31 memo signed by Kathleen B. Troia, principal deputy assistant secretary of defense for public affairs, and released by Common Cause. A separate memo obtained by The Washington Post shows that the Pentagon also plans to make "substantial use" of its internal media to sell the administration's management effort to military and civilian employes.

One event scheduled in the plan, a briefing for reporters on management reform, appeared to backfire somewhat yesterday when official charts showed that the Carter administration had made more progress in promoting competition and fixed-price contracts than the Reagan administration. The graphs had been drawn to show greater progress in recent years, but the numbers did not support the drawings.

The plan called for Weinberger to kick off the public phase of the campaign with a Sept. 18 speech to the American Newspaper Publishers Association. During that speech, delivered as planned, Weinberger complained that newspapers frequently print "horror stories" about weapons procurement but do not present the whole story, including the Defense Department's role in uncovering and correcting problems.

The memo also stresses that "local commanders" should be involved in the campaign as much as possible. "This is particularly important, since local press are often far more receptive to messages of this type than national media . . . ," it states.