Captain Rogelio Maynulet faces a charge of assault with intent to commit murder in the 21 May 2004 killing near Kufa, south of Baghdad.
Prosecutors say he violated the army's rules of engagement by shooting the Iraqi while he was unarmed and injured.
Maynulet, 30, has pleaded not guilty to the charge, which carries a maximum sentence of 20 years in prison.
One of Maynulet's superiors during his tour in Iraq said he was one of the "top three" of roughly 37 officers he oversaw at that time, describing him as "a tremendous soldier".
Colonel Bradley May told the court in written testimony read aloud on Tuesday that, while he agreed in principle against firing on the wounded, each case must be considered individually.
"To make that determination, we have to look at all the facts," May said in his statement. "It may be that some make it not as easy to determine as we would all like."
Film from a US drone surveillance aircraft showed the outline of a soldier in a helmet and battle gear, identified by a witness as Maynulet, aiming a weapon at an Iraqi man lying on the ground, followed by a flash.
A US drone showed the soldier
shooting the unarmed Iraqi
The man on the ground appeared to be waving his right arm before the shot. Several seconds later, he appeared to
twitch as though hit again.
Defence attorneys at the court-martial maintain that Maynulet, convinced the man would not live, shot him to end his suffering.
No medical treatment
Earlier on Tuesday, a US Army medic testified he had pulled the wounded Iraqi from a car that had crashed following a chase, but then failed to treat a severe head wound, instead telling Maynulet he would not live.
"You ignored him because you were freaked out, you told him (Maynulet) he's going to die?" defence lawyer Captain Will Helixon asked the medic.
"Yes, sir, that's correct, sir," replied Sergeant Thomas Cassady.
"Captain Maynulet has compassion toward the Iraqi people"
Major Yahay Haidar
Cassady said he had spent about one minute with the man, failing even to take his pulse or check his breathing.
Asked why he did not treat him, Cassady said: "I spazzed out at that instant."
In addition, Cassady conceded that he had lied during Maynulet's Article 32 hearing - the military equivalent of a civilian grand jury investigation - giving testimony about injuries the man had not suffered because he felt guilty about the incident.
"You felt guilty, that it was your fault because you didn't do your job," Helixon said.
Cassady responded: "That's correct, sir."
"You felt you should be the one in trouble," the defence attorney said.
"Correct," Cassady replied.
Maynulet's company had been on patrol when it was alerted to a car thought to be carrying a driver for cleric Muqtada al-Sadr and another fighter loyal to the cleric. They chased the vehicle and fired at it, wounding both the passenger, who fled and was later apprehended, and the driver.
In further testimony on Tuesday, two Iraqis who worked with Maynulet during his deployment to Iraq described him as compassionate and spoke of his helpfulness to civilians and Iraqi soldiers training for the civilian defence corps.
"Captain Maynulet has compassion towards the Iraqi people,"
Major Yahay Haidar said in written testimony read before the court. "Captain Maynulet cares for the Iraqis."
Such testimony plays an important role in a court-martial, where the six-member panel - the equivalent of a civilian jury - must also weigh whether the actions of the accused damaged the army's reputation.
Maynulet's command was suspended 25 May, but he has remained with his Wiesbaden-based unit.
The US military has referred to the Iraqi driver only as an "unidentified paramilitary member," but relatives named him as Karim Hasan, 36. The family does not dispute that he was working for al-Sadr.
The trial is to continue Wednesday.