Facebook and Twitter's chief executives have been cross-examined by US senators for the second time in three weeks.
The two were summoned to answer questions about how their platforms had limited distribution of a controversial article about Joe Biden's son published ahead of the US election.
But they have also been challenged over their handling of posts by President Trump and others who have contested the vote's result.
The tech firms face new regulations.
In particular, President-elect Biden has suggested that protections they currently enjoy under a law known as Section 230 should be "revoked" since it encourages the spread of falsehoods.
The law says the platforms are generally not responsible for illegal or offensive things users post on them.
Senator Lindsey Graham warned the social networks that "change is going to come"
Republicans also voiced concern at the hearing.
They said the social media companies were taking editorial decisions about what to take down, label or leave unaltered.
This, they said, made them publishers rather than just distributors of information, and as a consequence they should not be covered by Section 230 in its current form.
"Federal law gave you the ability to stand up and grow without being hit by lawsuits," said Republican Senator Blackburn.
"You have used this power to run amok."
Republican Senator Lindsey Graham, chairman of the Senate Judiciary Committee, added: "When you have companies that have the power of governments, have more power than traditional media outlets, something has to give."
The two tech CEOs began by defending their record over the recent US election.
But Mr Dorsey acknowledged that Twitter's decision to block links to the New York Post article about Hunter Biden had been "wrong", and that its failure to subsequently restore the newspaper's own tweets about the story had required a further policy change.
Twitter's Jack Dorsey: "Like anything else, these tools can be addictive"
"I hope this... demonstrates our ability to take feedback, admit mistakes and make all changes transparently to the public," he said
Mr Zuckerberg avoided direct reference to the matter in his opening remarks.
However, he used the opportunity to challenge recent claims by Democrats that Facebook had been slow in removing posts that promoted insurrection and violence.
"We strengthened our enforcement against militias and conspiracy networks like QAnon to prevent them from using our network to organise violence or civil unrest," Mr Zuckerberg said.
The two tech leaders were then both challenged over some of their recent decisions.
The Democratic Senator Richard Blumenthal wanted to know why Facebook had not banned Steve Bannon.
President Trump's former top advisor recently called for the beheadings of disease expert Dr Anthony Fauci and the FBI director Christopher Wray in a video he posted to both Twitter and Facebook.
Twitter threw him off its service, but Facebook only froze Mr Bannon's page.
Mr Zuckerberg said Mr Bannon "did violate our policies" but had not clocked up enough strikes to permanently lose access.
And when the senator called for a rethink, Mr Zuckerberg responded: "That's not what our policies would suggest we should do."
Mr Zuckerberg said he thought there was a role for regulation in Facebook's use of algorithms
Mr Zuckerberg went on to dispute reports that Facebook had forgiven infractions by both of Donald Trump's sons and the news site Breitbart, among others, in order to avoid accusations of bias from conservatives.
"Those reports mischaracterise the actions that we've taken," he said.
The Democratic Senator Dianne Feinstein followed up with questions to both executives over their responses to President Trump's posts about election fraud, which lacked factual basis.
She asked Twitter's chief whether he thought adding labels but allowing the tweets to remain visible went far enough.
Mr Dorsey responded that he believed providing "context" and "connecting people to the larger conversation" was the right path to follow.
Senator Feinstein went on to ask Mr Zuckerberg if he felt enough had been done to prevent people delegitimising the election's result given that hashtags for Steal The Vote and Voter Fraud had garnered more than 300,000 interactions on its platforms in the hours after Mr Trump falsely declared victory.
Senator Feinstein questioned whether labels do enough to counter misinformation
"I believe we have taken some very significant steps in this area," Mr Zuckerberg responded, pointing to information it had placed at the top of the screens of US-based Facebook and Instagram users.
"I think that we really went quite far in terms of helping to distribute reliable and accurate information about the results."
Voter fraud warnings
The Republican Senator Ted Cruz took a different tack, asking why Twitter was "putting purported warnings on virtually any statement about voter fraud".
When Mr Dorsey repeated his earlier point about linking people to conversations, Mr Cruz pushed back.
"No you're not. You're putting up a page that says 'voter fraud of any kind is exceedingly rare in the United States'. That's not linking to a broader conversation. That's taking a disputed policy position."
Mr Cruz added that Twitter had the right to take such a position, but only if it accepted it was a publisher and gave up Section 230's protections.
Senator Cruz said he planned to tweet about a case of alleged voter fraud in Texas to see how Twitter would respond
And he challenged both firms to disclose how many times they had blocked Republican and Democratic candidates for office in the 2016, 2018 and 2020 elections to reveal any discrepancy.
Neither tech chief would give a firm commitment to do so.
Republican Senator Joni Ernst later asked what the two tech leaders were doing to monitor the political views of their staff.
Both of the chief executives said this would be hard to do, but they suggested one consequence of the Covid-19 pandemic was they would have more people working from home in the long-term, which in turn should entail greater diversity among their workforce.