National Rifle Association officials, in a complicated internal struggle, have requested the resignations of Executive Vice President G. Ray Arnett and three of his closest aides because of what one NRA source described as "serious charges of mismanagement."

Arnett, in a statement released yesterday, described the NRA executive committee's weekend meeting at which he was fired as a "kangaroo court" and said it does not have authority under NRA bylaws to fire him. He suggested that he and the other fired officials will file a lawsuit against the organization that "will require a major investment of NRA resources."

Arnett, former assistant secretary of interior for fish, wildlife and parks, has indicated that he will step down from the NRA's top post only if the executive committee obtains a court order. As a result, the committee said yesterday, Arnett has been suspended without pay and will not be allowed to use NRA facilities or property.

"I don't think the NRA ever was intended to be run by a small group of individuals serving their own personal interests and agenda," Arnett said. "If the majority of the NRA membership did not want me to hold this position, I would step down."

Claiming that the NRA's 3 million members will be "enraged" by the decision, Arnett said, "I walked into a kangaroo court . . . . It's a travesty and I expect to see the action overturned."

NRA staff sources, who would speak only on condition that they not be identified, said the confrontation had been building for months.

The sources said one issue discussed by the executive committee was that from last September through January, Arnett had been absent from the office for long periods, using NRA facilities and funds for extended hunting trips.

During that period, the organization was conducting its heavily publicized and successful campaign to weaken the 1968 Gun Control Act.

The legislation, known as Volkmer-McClure, was signed into law yesterday by President Reagan.

Earlier this month, Arnett shocked the organization by abruptly firing the NRA's 17-member public education staff and hiring an outside public relations agency. Arnett informed the employes of his decision on the morning of May 7 and ordered them to clear their desks and leave the building by noon.

The firings came one day after the Senate approved the NRA-supported gun bill that most of the fired staff members had worked for.

Under the resolutions adopted by the committee, the public education staff fired by Arnett will be rehired.

In his statement, Arnett did not address any specific allegations, which he called "broad and unsubstantiated," but said that during the committee meeting, "I answered every allegation honestly and completely."

During Arnett's suspension, J. Warren Cassidy, who had headed the NRA's lobbying arm, will take over Arnett's duties and become acting executive vice president. Wayne R. LaPierre Jr. has been named to take over Cassidy's job as head of the Institute for Legislative Action.

NRA spokesman Andrew Kendzie said yesterday that Cassidy and LaPierre "enjoy the full support" of the NRA staff.

The executive committee also fired staff director Morton C. Mumma III, administrative services director John C. Bartholf and personnel director Frederic H. Smith III by abolishing all three positions immediately.

Harlon B. Carter, who previously held Arnett's position and is seen as a father figure in the NRA, will come to Washington as a consultant to help the organization until leadership problems are worked out.