ap photo Facebook CEO Mark Zuckerberg testifies remotely during a Senate Judiciary Committee hearing on Facebook and Twitter’s actions around the closely contested election on Tuesday in Washington.

WASHINGTON — As the CEOs of Twitter and Facebook gave assurances of vigorous action against election disinformation, Republicans at a Senate hearing Tuesday pounded the social media companies over political bias, business practices and market dominance, laying the ground for curbs on their long-held legal protections.

Twitter’s Jack Dorsey and Facebook’s Mark Zuckerberg defended at the Senate Judiciary Committee hearing the safeguards against the use of their platforms to spread falsehoods and incite violence in the contest between President Donald Trump and Democrat Joe Biden. Responding to concern from Democrats on the panel, they pledged continued vigorous action for two special elections in Georgia that could determine in January which party controls the U.S. Senate.

Republican senators, including Committee Chairman Sen. Lindsey Graham, revived complaints of censorship and anti-conservative bias against the social media platforms. They were reticent to address head-on the issue of election disinformation, an awkward topic for Republicans given that many of them have refused to knock down Trump’s unfounded claims of voting irregularities and fraud, even as misinformation disputing Biden’s victory has flourished online.

The actions that Twitter and Facebook took to quell the spread of disinformation angered Trump and his supporters.

Different grievances but a common adversary. Democrats, including President-elect Biden, also call for stripping away some of the protections that have shielded tech companies from legal responsibility for what people post.

They have focused their concern on hate speech and incitement on social media platforms that can spawn violence.

Sen. Mazie Hirono, a Democrat from Hawaii, asked Zuckerberg: “At what point will you stop giving in to baseless claims of anti-conservative bias and start exercising your control over Facebook to stop driving division?”

Graham pushed the case for Congress to curb the tech companies’ legal shield. “I think there’s Republican and Democrat concern about the power that’s being used by social media outlets to tell us what we can see and what we can’t, what’s true and what’s not,” Graham said.

Republicans and Democrats also are making common cause on Big Tech’s market dominance, endorsing stronger enforcement of antitrust laws and for some, the breakup of giants like Facebook and Google.

“Your companies are the most powerful in the world,” Sen. Josh Hawley, a Missouri Republican, told Dorsey and Zuckerberg.

“It is time we took action against these modern-day robber barons,” Hawley said, referring to the 19th century industrial moguls whose ruthless practices built fortunes.