Rep. Jim Matheson (D-Utah) introduced a bill this week that would ban the sale of violent video games to minors.
The Supreme Court struck down a similar California law in 2011, ruling that the restriction violated the constitutional right to free speech.
Matheson's Video Games Ratings Enforcement Act, H.R. 287, would make it illegal for anyone to ship, distribute, sell or rent a video game that does not bear a label from the Entertainment Software Ratings Board (ESRB) on the age-appropriateness of the game.
It is currently up to retailers to decide whether to sell violent or sexually explicit games to minors.
Matheson's bill would make it illegal to sell or rent video games with a rating of "adults only" to anyone under 18, or video games rated "mature" to anyone under 17.
The measure would also require retailers to display information from the Federal Trade Commission about the ESRB's content-rating system in a "clear and conspicuous location."
In the wake of last month's mass shooting at a Connecticut elementary school, a number of lawmakers have expressed concern about the influence of violent video games on young people.
On Wednesday, President Obama called on Congress to appropriate money to study whether video games contribute to real-world violence.
In a phone call, Matheson told The Hill that he offered similar legislation in past sessions and that he had been working on a new draft of the bill before last month's shooting.
But he said the shooting "provides additional need to at least talk about this issue."
In the 2011 decision striking down the California law, the Supreme Court concluded that video games are protected under the First Amendment.
“Like the protected books, plays and movies that preceded them, video games communicate ideas — and even social messages,” Justice Antonin Scalia wrote in the court's opinion.
He said that California's argument that it could restrict speech directed at children is "unprecedented and mistaken."
"No doubt a state possesses legitimate power to protect children from harm ... but that does not include a free-floating power to restrict the ideas to which children may be exposed," Scalia wrote.
Matheson argued that his bill is different than the law the court struck down because California had tried to define violent video games, whereas his measure relies on the industry's own rating system.
"I'm not a lawyer myself, and I'm not going to tell you that that's going to change the constitutional question necessarily," he said.
He noted that the government regulates access to pornography, and he said finding the right balance between respecting free speech and protecting children is a "discussion that's got to continue."