The department also will issue proposed rules within 60 days that make clear that devices marketed as "stabilizing braces" will be subject to the National Firearms Act.
The suspect, Aminadab Gaxiola Gonzalez, was also charged with three attempted murder counts for firing at two officers and critically wounding the mother of a boy who was killed.
The violence in the city of Orange was the third major mass shooting in just over two weeks in the U.S.
The ruling on the National Rifle Association-backed lawsuit challenging the ban came under a Colorado law that bars local officials from making their own gun laws.
Those who lost their lives at the King Soopers store in Boulder ranged from 20 years old to 65.
The second deadly U.S. mass shooting in a week is putting new pressure on President Joe Biden to deliver on the gun control promises he made as a candidate.
The NRA fought to block a ban on assault-style rifles in Boulder, Colo., less than two weeks before 10 people died in a mass shooting at a supermarket.
``In seconds, the lives of dozens of families, and the life of an American community, were changed forever,'' Biden said in a statement released Sunday.