WASHINGTON—Suspected Navy Yard shooter Aaron Alexis lied during the security-screening process when he joined the military and misled investigators about an incident that led to an arrest, according to documents released Monday by the Pentagon.

A continuing U.S. Navy review of Mr. Alexis's military career has revealed he failed to disclose his arrest in Seattle in 2004 for shooting out a car's tires and, when confronted about the arrest, never told investigators he used a gun.

The examination of last week's shooting revealed more gaps in the federal government's troubled security-screening process, which the Pentagon, White House and Congress are all scrambling to fix.

Military officials are trying to figure out how they missed a series of red flags that might have allowed them to intervene and prevent Mr. Alexis from securing a job as a military contractor at the Washington Navy Yard, bringing a shotgun onto the secure facility and killing 12 people before being shot dead by police.

A central focus of the review is a 2007 background check of Mr. Alexis conducted by US Investigations Services LLC, a Falls Church, Va., company facing a criminal investigation over allegations that it rushed cases through the clearance process without proper review.