The defendant may face life in prison without possibility of parole.
Cortez was the second to plead guilty in the killings, one of the most high profile of several atrocities allegedly committed by US troops in Iraq.
Last November, Specialist James Barker was sentenced to 90 years in prison as part of a plea deal in the case.
On Wednesday, prosecutors and the defence in the military court argued the last outstanding charge against Cortez; whether the four murders were premeditated.
After lengthy debate, the judge moved to drop the action, allowing the court to move forward to sentencing on five charges of premeditated conspiracy to commit rape, four counts of felony murder, rape, violation of a general order (consuming alcohol) and breaking into a house.
The hearing will resume on Thursday morning, with the court expected to hear mitigating arguments on sentencing.
Two other soldiers in the case are awaiting military courts martial, while a fifth, who was discharged from the army before the case came to light, will be tried in federal court at a later date.