WASHINGTON – The Supreme Court said Tuesday that it will not hear a closely watched case against gunmaker Remington, a move the company has warned could potentially increase the liability of firearm manufacturers to suits brought by victims of gun crimes.

The court's action will allow the family members of children killed in the 2012 Sandy Hook Elementary school massacre in Connecticut to move forward with their lawsuit. The shooting left 20 children and six adults dead.

The families sued the makers of the gun that was used, an AR-15-style weapon made by Remington, in 2014, alleging that the company's marketing of the weapon inspired Adam Lanza to commit the massacre.

Read more: CNBC's Remington Under Fire series

Remington argued that its actions were protected under a 2005 law that shields gun makers from liability for crimes committed with their products. That law, the Protection of Lawful Commerce in Arms Act, has come under new scrutiny amid a rise in mass shootings.

An exception in the law, provided in cases where the gun manufacturer knowingly violated the law through its marketing practices, paved the way for the families to launch their suit. They claim that Remington marketed the weapon "as a highly lethal weapon designed for purposes that are illegal — namely, killing other human beings."

The Connecticut Supreme Court ruled in a divided opinion earlier this year that the family members could pursue their lawsuit, rejecting Remington's argument. The court wrote that the family members are "entitled to have the opportunity to prove their wrongful marketing allegations."