CINCINNATI, March 19 — Responding to a series of scandals, Ohio’s new secretary of state said Monday that she had demanded the resignation of the entire four-member Elections Board of Cuyahoga County, which includes Cleveland.

Just last week, in the latest development involving one of those scandals, two former Cuyahoga elections workers were sentenced to the maximum of 18 months in jail for manipulating a preliminary recount of the 2004 presidential election vote. The workers’ goal had not been to affect the outcome but rather to avoid a more painstaking task in which all votes would have had to be recounted by hand rather than machine.

“When you have election workers going to prison for election-related offenses, it creates a crisis of confidence,” the secretary of state, Jennifer L. Brunner, said in announcing that she spoke to the four board members Sunday night to urge them to resign. If they do not do so by Wednesday evening, Ms. Brunner said, she will begin a disciplinary process Thursday morning to force their ouster.

Ms. Brunner was elected in November as part of a near sweep of state offices by Democrats that reversed a Republican lock on statewide posts. The board she seeks to remove has two Democratic and two Republican members, including Robert T. Bennett, chairman of both the board and the Ohio Republican Party.