His attorneys are challenging evidence gathered in last June's killing of semi-pro football player Odin Lloyd.
They asked a Fall River judge to exclude surveillance video from Hernandez's North Attleborough home. They also want evidence seized from cellphones and other electronic devices kept out of the case.
Prosecutors countered that the evidence is "powerful."
A tentative trial date of Oct. 6 has been set for the Lloyd murder case.
Also Monday, Hernandez pleaded not guilty to charges that he attacked a handcuffed inmate and threatened to kill a guard and his family while at a county jail in Dartmouth.
Hernandez also is charged with killing two men in Boston in 2012.
The Associated Press contributed to this report.