In 1961, after years of denying rumors that he sought a higher public office, Celebrezze was offered a federal judgeship by President John F. Kennedy, which was a lifetime appointment to a federal judgeship. Celebrezze turned it down to run for a record-breaking fifth consecutive term as mayor, which he won by an unprecedented 73.8 percent, sweeping every one of the city's thirty-three wards. Kennedy appointed him also to serve on the Committee on Equal Employment Opportunity and the Commission on the Status of Women. In 1962, Celebrezze was selected as the president of the United States Conference of Mayors.