The Twitter logo is displayed on a screen on the floor of the NYSE. Thomson Reuters

Family members of three Americans killed by ISIS attacks in Belgium and France have sued Twitter for allegedly failing to keep members of the terrorist organization off its platform.

The lawsuit, which was filed in the southern district of New York on January 8, alleges that Twitter has played "a uniquely essential role in the development of ISIS’s image, its success in recruiting members from around the world, and its ability to carry out attacks and intimidate its enemies."

Lawyers representing the plaintiffs argue in court documents that Twitter violated the Anti-Terrorism Act, and they are asking for "compensatory damages in amounts to be determined at trial."

A Twitter spokesperson didn't respond to a request for comment about the case. A similar lawsuit accusing Twitter of providing support to ISIS was dismissed by a California judge in August 2016. The company is currently facing another similar lawsuit by family members of victims killed in the June 2016 attack at the Pulse nightclub in Orlando, Florida.

Twitter has long been criticized for its inability to keep terrorists off its network. A 2014 article in The Atlantic titled "How ISIS Games Twitter" described how "extremists of all stripes are increasingly using social media to recruit, radicalize and raise funds."

Twitter began cracking down on accounts related to ISIS in the summer of 2015, when it suspended 125,000 accounts in one fell swoop. In August 2016, the company said it had suspended a total of 350,000 accounts related to ISIS since mid-2015.

Despite Twitter's uptick in banning, the January 2017 lawsuit alleges that the company has "continued to provide these resources and services to ISIS and its affiliates, refusing to actively identify ISIS Twitter accounts, and only reviewing accounts reported by other Twitter users."

"Simply put, ISIS uses Twitter as a tool and a weapon of terrorism," the suit argues.