Facebook, Twitter and Google's chief executives received more than three and a half hours of questions from US senators on Wednesday.
At present, it is not possible to sue businesses for what their customers share online, or the choices they make about what to leave and takedown.
Some lawmakers have expressed fears that poor conduct is promoted by this "sweeping immunity".
But the chief executives say that to be able to moderate content, they need the rule.
After both Democrats and Republicans decided to bring them in for interrogation, Facebook's Mark Zuckerberg, Twitter's Jack Dorsey, and Google's Sundar Pichai were called before the Senate.
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