Twenty potential jurors were summoned to the courtroom at Fort Hood and six of them dismissed, CNN reported. The remaining 14 are to be questioned Wednesday.
Potential jurors will be brought in every week 20 at a time until a jury has been selected, military officials say. Opening statements are scheduled for Aug. 6.
Hasan, 42, could be sentenced to death if he is convicted of killing 13 people at Fort Hood in November 2009 and wounding many more.
Col. Tara Osborn, the judge at the court-martial, has refused to allow Hasan to use as a defense that he carried out the killings to prevent the unlawful killing of members of the Taliban in Afghanistan. He had been scheduled for deployment there in late 2009.
Osborn has not yet ruled whether Hasan can tell jurors he is "forced" to wear the U.S. Army uniform. He told Osborn Tuesday the uniform represents "an enemy of Islam," the Austin American-Statesman reported.
"I can't take any pride in wearing this uniform," Hasan said. "I want the panel to know that, that I am being forced to wear it."