West German Defense Minister George Leber offered to resign yesterday in a growing scandal involving illegal bugging operations by Bonn's military counterintelligence service.

Leber, 50, has been the West German defense minister of 5 1/2 years. He is the senior defense chief within Nato and has become a major spokesman for the alliance, especially in the past two years. His loss undoubtedly will be felt at NATO headquarters.

The disclosure of the bugging operation also closely follows a related scandal involving East German spies on the Defense Ministry, which produced what was probably the most serious breach of security in the post-war history of Bonn's defense forces. The reverberations were felt by Leber, his ministry, the Bonn government and NATO.

Chancellor Helmut Schmidt asked Leber to reconsider his resignation and make a report today to a specially convened clsoed meeting with heads of all major parties in the Bonn Parliament.

The political effect that the controversy surrounding Leber will have on Schmidt's government is unclear.

Schmidt himself personally remains quite strong according to all public opinion polls and the conservative oppostion leaders are too weak in comparison. Schmidt's party is being rocked by the defense scandals and others in two major state-owned banks.Elections are sufficiently far away, however, that the current problems could well fade from voters's memories.

Leber offered his resignation after a Cabinet meeting in Bonn yesterday, saying that he had misled Parliament about the extent of the illegal bugging and that he accepted political responsibility for misinforming the legislators.

Leber had told Parliament last week during an "investigation of the spying episode, that he knew of only one instance when the military counterintelligence service installed a bug - or electronic listening device - illegally.

Yesterday, however, he told the Cabinet that he had since learned that there had been other such cases. He did not say how many, but a report on West German television tonight said that there may have been up to 20.

Leber, a generally conservative member of Schmidt's ruling Social Democratic Party, has been in trouble for some time with the party's left wing. But he is widely respected as defense minister and is well-liked within the West German forces and in NATO.

His trouble began in December with the disclosure that three alleged spies working in his ministry had access to top secret material for several years and were apparently passing it on to East Germany.

The spies were caught in mid-1976, but the dimensions of their espionage were disclosed by a newspaper only two months ago. Afterward, Leber admitted he had learned of the extent of the spying from the newspaper report and had not read preliminary reports of the damage prepared by his own service.

Later, it was disclosed that the telephone of one of Laber's personal secretaries had been tapped in 1975 by military agents who thought she might be a communist spy This tap was legal and Leber had approved it. The woman was cleared.

Leber said, however, that he learned early in 1977, that the counterintelligence agents also had illegally bugged the secretary's apartment in 1975.

It was this single illegal bugging that Leber told Parliament about last week.

Despite Schmidt's request that Leber reconsider his resignation, it is viewed as highly unlikely that the defense minister will survive the mounting controversy.

He has been under sharp attack from opposition leaders and other who accuse him of minimizing and trying to cover up the facts in both the spy case and the bugging, and his tense performance since the storm broke around him has not impressed many top Social Democratic leaders.

Leber and other government officials have sought to point out in the spying cas that the central figure was actually hired under the previous conservative administration and was apprehended under Leber.

Leber, shortly after hearing of the illegal apartment bugging early in 1977, ordered the early retirement of the counter intelligence chief who ordred the bug placed.