A feud with potentially serious implications is developing between Defense Secretary Harold Brown and some high-level Army officers and civilian officials.

The situation is being fed by what each side sees as misstatements by the other during an election campaign in which the subject of military readiness and the adequacy of military budgets have become bitter issues dividing the forces of President Carter and Republican challenger Ronald Reagan.

The dispute came into sharper focus yesterday in the aftermath of a major speech in El Paso, Tex., last week by Brown and a speech here Tuesday by the Army Chief of Staff Gen. Edward C. Meyer.

Brown's speech was meant as a major Carter administration rebuttal to critics who claim that defenses have been allowed to slip in the last four years. Brown said that such claims are misleading and that the United States is ready to fight if necessary, and he listed numerous details to show that the military has not been standing still.

Yesterday, however, defense officials acknowledged that Brown "misspoke" on at least one major project. "Beginning next year," he had told the El Paso audience, "the Army's fleet of 1,000 powerful Cobra-TOW attack helicopters will be augmented by the Advanced Attack Helicopter," the more potent successor to the current chopper force.

Officials say that the first of these new missile-firing helicopters will not be delivered until 1983, two years later than Brown said, and that only about half of the 1,000 or so Cobras are equipped to fire the TOW antitank missile.

There have also been some press reports in recent days, and questions asked by reporters at Pentagon briefings, suggesting that unnamed Army budget officials are upset because Brown did not mention various cutbacks in projects in his optimistic accounting of U.S. strengths. The fact that some people in the Army are taking hard shots at Brown in private is clearly annoying the defense chief, his aides confirm.

Defense officials say, however, that Brown's only slip was in that one sentence about helicopters in a 5,000-word speech and that this is hardly grounds for internal attacks upon the secretary's integrity. They will not discuss in any detail some of the other allegations that have appeared in print, but they claim that all of them are either incorrect or misleading and are connected with a fiscal 1982 budget in which final decisions are not yet made. Defense officials see this as traditional service maneuvering to get a bigger slice of the budget around this time.

There is special annoyance in Brown's office with the Army.

On Tuesday, Gen. Meyer, in a speech to the Association of the United States Army, called attention to what he called the "harsh facts of life today -- the fact that the Army's share of the defense budget has shrunk to just a little over 24 percent, the lowest in more than 16 years."

Defense officials suggested Meyer was over-dramatizing.

"The underlying issue seems to be a lament . . . by some people in the Army . . . that the Army is not getting its fair share of the pie," said Thomas B. Ross, Brown's assistant secretary of defense for public affairs. "The fact is we are talking about a 1 percent fluctuation." Ross provided statistics yesterday to show that while Meyer is technically correct, the difference in the Army share this year as opposed to last year was 1 percent and that for the past five years there is less than a 1 percent variation from today's Army share of the budget.

Furthermore, they claim more recently adjusted data as of July show the current Army share of the overall Pentagon budget slightly larger than it was in 1977.

On Capitol Hill, sources familiar with the escalating battle point an accusing figure at both the Pentagon and the Army in this dispute. They argue that many programs have been underfunded throughout several administrations in terms of what they were supposed to accomplish and that the Army itself has been especially incompetent in getting fancy and highly technical new weapons through the development process and into the field.

Military reports indicating that six out of 10 Army divisions based in this country were not combat-ready also were leaked to the press several weeks ago, causing Brown some embarrassment and requiring him to make lengthy explanations in public.

This escalating level of hard feelings is worrying all sides in the Pentagon. It is clear within the top civilian echelons of the Pentagon that they fear some people within the services are not only trying to use this campaign period to get a bigger slice of the budget but that they are also providing ammunition for Ronald Reagan.

Within the Army, some experienced officers say they are extremely unhappy to see stories in the press in which unnamed Army officials are alleging Brown is behaving differently than his speeches suggest. Their fear, too, is political. Whether or not those allegations are true, they worry about retribution directed at the Army brass and budget in a second Carter administration.