FBI Director William H. Webster yesterday reversed his decision to fire an FBI supervisor charged with misconduct while pursuing the radical Weather Underground in the early 1970s.

Webster announced he was changing the dismissal to a demotion. He said an administrative appeal convinced him that the agent had been "open, candid and cooperative" and was considered "crucial" to the success of the internal investigation of allegedly illegal FBI break-ins used in searching for the fugitive bombers.

Though the FBI did not name the supervisor, sources identified him as Horace Beckwith, a popular 46-year-old agent who once headed the New York squad chasing the Weather Underground.

Webster said his announcement "also serv es as an incentive to others to cooperate with legitimate administrative inquiry."

A key consideration in changing Webster's mind, sources said, was a letter from Frank Martin, one of the prosecutors in the case, which outlined Beckwith's cooperation.

Brian P. Gettings, Beckwith's attorney, said yesterday that his client "looks forward to returning to a field office to become a street agent again. He hopes to be able to justify the faith the director has shown in him."

Beckwith will suffer a pay cut of about $4,000 a year when demoted to the field, sources said.

Webster announced in December that he was disciplining four FBI supervisors for their role in the investigation of the Weather Underground. At the time Webster said -- without naming him -- that Beckwith was being fired for approving bread-ins without approval from headquarters and for having ignored instructions by approving electronic surveillances and mail openings.

In a letter to Attorney General Griffin B. Bell yesterday, Webster noted that the other supervisor to be fired -- identified as Brian Murphy -- "was permitted to retire." The other two men accepted demotion and suspension, Webster said. The 58 street agents involved in the administrative inquiry were not desciplined, Webster said then, because they were obeying orders.

Gettings said yesterday that "if everyone in the (Weather Underground) investigation had cooperated like Horace there never would have been a grand jury or the indictments that followed."

Gettings is also the attorney for W. Mark Felt, one of three former top-ranking FBI officials scheduled to go on trial March 5 for violating the civilrights of friends and relatives of the Weather Underground fugitives by approving break-ins and other surveilance. Former acting director L. Patrick Gray III and Edward S. Miller, former head of the bureau's intelligence devision, are the other defendants.

Their trial has been delayed while defense attorneys and prosecutors argue over the relevance of classified material. The defendants contend the sensitive documents will show that any acts in pursuit of the radical fugitives were justified because of the group's ties to foreign powers.