A major spy scandal in West Germany widened today when government prosecutors announced that a secretary in the president's office had been arrested on suspicion of spying.

The secretary's arrest, which took place yesterday, followed the defection last week of one of the country's leading counterintelligence officers and the disappearance of three other suspected East German agents.

A spokesman for the federal prosecutor specified that the secretary did not serve as a personal assistant to President Richard von Weiszaecker. One of the vanished spy suspects, Sonja Lueneburg, worked for 12 years as the private secretary and political confidant of Economics Minister Martin Bangemann.

But security sources said the presidential staff secretary, who worked under von Wieszaecker's chief aide for defense and foreign affairs, had access to highly classified material. They said she would have seen all communications from West German embassies and reports on the president's talks with foreign leaders and dignitaries.

The secretary, described as in her early fifties and unmarried, was kept under surveillance for several weeks after it was learned she was acquainted with a known East German intelligence agent, security officials said. She is said to have spent two weeks in Copenhagen recently in the company of the agent.

The prosecutor's spokesman also said investigators were looking into a possible espionage case at an Army weapons procurement office in Koblenz but said no arrests had been made yet.

West German security experts have warned that the spreading spy scandal could induce other East German spies to flee. They said that counterintelligence officials would have to move quickly to seize suspected agents before they tried to reach sanctuary in East Germany.

All spy suspects known to authorities, including some other Bonn secretaries, are said to have been placed under close watch in case they attempt to leave West Germany. Security experts forecast more arrests in the coming days.

As Chancellor Helmut Kohl's government pursued an emergency security review to cope with the damage inflicted by the far-reaching espionage case, security officials said there were indications that Hans Joachim Tiedge, who was in charge of tracking East German spies inside West Germany, probably became a Communist agent two years ago.

The sources said that Tiedge is believed to have passed along information since 1983 that led East German authorities to seize nearly 200 western intelligence contacts in East Germany.

Besides the wave of arrests, investigators said other factors suggesting that Tiedge may have switched allegiances two years ago were his decline into debt and drinking problems after his wife's death in 1982 and his department's failure to apprehend any important East German spies in that time.

The crash security review, overseen by Interior Minister Friedrich Zimmermann since Friday, has focused on steps to curtail the damage that could be wrought by Tiedge's cooperation with East German intelligence.

Zimmermann said today that "a new concept for combating East Bloc espionage, in particular against the activities of East German services," will be required to overcome the effects of Tiedge's betrayal.

The minister said he had instructed the country's counterintelligence chiefs to begin immediately a complete reorganization of the internal security network and to develop "new operative investigation methods."

Security experts said that apart from betraying West German intelligence strategy and techniques, Tiedge was in a position to inform East German authorities about double agents, estimated to number 200, dispatched to the West by East Berlin and turned by Bonn's counterspy operatives.

Zimmermann, who is to report to Kohl Monday on the implications of the spy scandal, said that a major personnel shake-up in the intelligence services probably would be carried out next week.

West German commentators predicted today that Heribert Hellenbroich, who until this month headed all counterspy operations and served as Tiedge's supervisor, was almost certain to be fired from his new position as chief of foreign intelligence.

Hellenbroich, a respected figure in his profession, knew of Tiedge's difficulties but reportedly refused to heed warnings from Tiedge's neighbors and coworkers that he was becoming a security risk. The two men conducted their early training together and had been friends for two decades.

As the third-ranking official in the Office for the Protection of the Constitution, Tiedge was in charge of the work of about 100 people, including several top counterspies who now may have to be reassigned.

Tiedge's decision to defect, it is now believed, may have been triggered by an order from the new counterintelligence chief, Ludwig-Holger Pfahl, to conduct rigorous new security checks on key staffers.

Besides his known alcoholism and health troubles, Tiedge is said to have left debts in excess of $80,000. Police searching his house after his flight discovered unpaid bills amounting to nearly $14,000.