White House denies assertions by leading investigator into the abuse scandal.
Jordan, 51, has pleaded innocent to illegally approving the use of dogs and nudity during interrogations, and allowing the mistreatment of Abu Ghraib prisoners to continue.
He faces up to eight-and-a-half years in prison if found guilty on the four remaining charges.
Jordan has argued that he is a scapegoat who, because he is a reservist, is considered expendable.
|The Abu Ghraib abuse scandal was a major
embarassment for the US administration [AP]
Opening the hearing at Fort Meade, Maryland, on Monday Judge Army Colonel Stephen R Henley granted the government’s motion to dismiss two charges after an investigator admitted to not reading Jordan his rights during a 2004 interview.
The two dropped charges are for making a false official statement, and for falsely swearing and obstructing justice.
The court-martial was triggered by photographs showing low-ranking US soldiers assaulting and humiliating naked detainees at the prison in Iraq in late 2003 and early 2004.
Jordan, who was not in any of the pictures, was in charge of the prison’s interrogation centre.
The Abu Ghraib scandal became a major embarrassment for the US, and struck a particularly harsh note among Iraqis because the prison under the rule of Saddam Hussein had been synonymous with the torture and killings of inmates.
During Monday’s opening hearing the court was told that Major-General George Fay, the investigator, had informed prosecutors he had “misspoke” during a pre-trial hearing in March when he claimed that he had read Jordan his rights.
Prosecutor Lieutenant-Colonel John P Tracy said Fay told government lawyers “he indeed did not read Lieutenant Colonel Jordan his rights”.
Judge Henley then ordered Jordan‘s statements to Fay to be suppressed before dismissing the two charges based on the 2004 statement in which Jordan said he never saw detainees being abused and never saw nude detainees.
Jordan still is charged with disobeying Fay’s order barring him from discussing the investigation with others, in addition to a failure to obey a regulation; cruelty and maltreatment of detainees; and dereliction of duty.
Eleven enlisted soldiers have been convicted of crimes at Abu Ghraib.
The longest prison term of 10 years was given in 2005 to former Corporal Charles Graner Jr for assault, battery, conspiracy, maltreatment, indecent acts and dereliction of duty.
Opening statements in Jordan‘s case are due to begin on Tuesday.