WASHINGTON — Federal prosecutors asked a judge on Tuesday to sentence James E. Cartwright, a retired Marine Corps general and former vice chairman of the Joint Chiefs of Staff, to two years in prison for lying to F.B.I. agents about his discussions with reporters about Iran’s nuclear program.

The Justice Department’s request to Judge Richard J. Leon, of Federal District Court for the District of Columbia, was significantly harsher than what prosecutors had agreed was the normal sentencing guideline range — a year of probation to six months in prison — when General Cartwright pleaded guilty to that charge in October to settle a four-year leak investigation.

Although the general was convicted only on a charge of lying to investigators as part of his plea deal, prosecutors argued that his case should be seen as a leak case and that a two-year sentence would serve as a deterrent by showing “that disclosing such information to persons not authorized to receive it has severe consequences.”

Lawyers for General Cartwright told the judge their client should not go to prison. They said he had already suffered grievous damage to his reputation and significant lost income and should be sentenced to a year of probation and 600 hours of community service.