Warren testified on Monday that he feared for his life when he shot Glover because he thought he saw a gun in his hand, but prosecutors said Glover wasn't armed and didn't pose a threat.
Jurors deliberated for about six hours Tuesday before adjourning for the night. They will reconvene Wednesday.
U.S. District Judge Lance Africk sentenced Warren to nearly 26 years in prison after a different jury convicted him of manslaughter in 2010. But a three-judge panel from the 5th U.S. Circuit Court of Appeals overturned his convictions last year, ruling that Warren should have been tried separately from four other former officers who were charged in an alleged cover-up of Glover's death.
Another former officer, Gregory McRae, was convicted in 2010 of burning Glover's body in a car after a good Samaritan drove the dying man to a makeshift police station. The same 5th Circuit panel that ordered a new trial for Warren also upheld McRae's convictions.
Jurors for Warren's retrial were barred from hearing any testimony about the alleged cover-up, including any references to the burned body. Warren wasn't charged with participating in a cover-up.
Jurors also heard testimony from a former officer, Alec Brown, who said Warren told him shortly after the shooting that he believed looters were "animals" who deserved to be shot. Warren denied saying that.
Earlier on the same morning as Glover's shooting, Warren had fired what he called a "warning shot" at a man who had been riding a bike near the mall. Warren said he knew officers aren't allowed to fire warning shots, but was worried the man intended to do "something stupid" because he had circled the mall several times.