A federal judge said he would rule within a week on a lawsuit requesting that New Jersey voters choose Gov. James E. McGreevey's (search) interim replacement in a special election.

U.S. District Judge Garret E. Brown Jr. heard arguments Wednesday in the suit filed by two Princeton lawyers who contend that McGreevey essentially vacated his office when he announced Aug. 12 that he was gay, and said he had an extramarital affair with a man and intended to resign Nov. 15.

By staying in office until it is not possible to hold a special election (search), he is depriving voters of their constitutional rights, lawyers Bruce Afran and Carl Mayer said.

Lawyers for the state argued that McGreevey has not officially resigned because he hasn't submitted a letter of resignation. They also argued that the issue is a state matter and should be determined in the state court system.

Brown said he would rule Tuesday or Wednesday next week.

Under state law, if McGreevey had left office before Sept. 3, a special election would have been called for Nov. 2. Because he outlasted the September deadline, Senate President Richard J. Codey (search) -- a fellow Democrat -- will serve as acting governor until the term expires in January 2006, unless the courts intervene. The state has no lieutenant governor.