In all, four current and one former soldier were charged with gang raping Abeer Qassim al-Janabi and murdering her and her family, a crime that outraged Iraqis and ratcheted up tension in the war zone.
The Mahmudiya case was one of several killings and abuses involving US soldiers. It prompted Iraqi officials to call for a review of foreign troops' immunity from prosecution in Iraq.
Specialist James Barker pleaded guilty in November and was sentenced to 90 years in a military prison.
In the plea agreement, Cortez said he held the girl's hands while Barker raped her, then he raped her himself.
The suspected ringleader, Steven Green, shot to death the girl's father, mother and six-year-old sister. He then raped the girl while Cortez acted as a lookout. Green finally shot the girl dead, according to the plea agreement.
Cortez, wearing a dress green uniform and flanked by his civilian lawyer and his military lawyer, showed little reaction to the judge's recitation of the crime. Fewer than two dozen spectators attended the trial in a tiny courtroom inside a Kentucky military base.
Despite his guilty plea, Cortez did not agree that the rape and murder were premeditated. His lawyer, William Cassara, said prosecutors will try to prove on Wednesday that the crime was planned ahead of time.
Alex Pickands, the prosecuting lawyer, said the soldiers "gathered together over cards and booze" last year in Baghdad and came up with a plan to rape and murder the girl.
Even if premeditation is not proven, the sentencing options are the same: a maximum of life in prison without parole or a minimum of life in prison with the possibility of parole. Barker and Cortez both avoided the death penalty by pleading guilty. Sentencing is expected on Wednesday or Thursday.
The trial was adjourned after less than three hours so that lawyers could discuss Cortez's involvement in the burning of the girl's body in an attempt to cover up the attack. Cortez pleaded guilty to arson and breaking into the girl's house.
The suspected ringleader, Green, was discharged from the army for a "personality disorder" and is in a Kentucky prison awaiting civilian trial.
Cortez also pleaded guilty to helping get rid of the murder weapon, an AK-47, which was thrown into a canal. He also admitted to drinking whisky prior to the attack, a violation of army rules against alcohol in that area of Iraq.
The other soldiers accused in the case are Private Jesse Spielman and Private Bryan Howard.