In a hearing in Washington, the social network chief was accused of letting political disinformation spread ahead of the 2020 US presidential election.
But he did say it was not his job to police what politicians said.
The tech boss was appearing before the House Financial Services Committee to defend plans for his embattled digital currency Libra.
But he found himself under attack over host of other issues, including failing to stop child exploitation on the social network and the Cambridge Analytic data scandal.
On the social network‘s policy on political ads, Democrat Alexandria Ocasio-Cortez asked: “I just want to know how far I can push this… could I run ads targeting Republicans in primaries saying that they voted for the Green New Deal?”
The Green New Deal is a Democrat policy fiercely opposed by most Republicans.
Mr Zuckerberg said the platform would take down posts from anyone, including politicians, that called for violence or tried to suppress voter participation.
As for untruths, however, he said it was not Facebook’s role to prevent “people in an election from seeing that you had lied”.
In another example, Democrat Sean Casten asked if Facebook would remove hate speech in political ads. He noted a former member of the American Nazi Party had run for Congress and won a Republican primary in 2018.
Mr Zuckerberg said: “Congressman, I think that depends on a bunch of specifics that I’m not familiar with this case and can’t answer to.”
“Well, that’s rather shocking,” said Mr Casten. “I don’t think that’s a hard question.”
The chief executive was also asked whether Facebook would remove ads that falsely claimed immigrants who participated in the US census would have their details shared with Immigration and Customs Enforcement (ICE).
What did he say about Libra?
Mr Zuckerberg also tried to reassure sceptical US lawmakers about the safety of his proposed digital currency Libra, but was given short shrift by most.
The project has faced a series of challenges recently, with key partner organisations having pulled out and mounting regulatory opposition.
Members of Congress raised concerns about whether currency could be used for money laundering, disrupt the global financial system, or give Facebook too much control over data.
Mr Zuckerberg said he was determined to persevere with the plan, arguing it could help more than a billion adults without a bank account worldwide.
But he added: “I get that I’m not the ideal messenger for this right now. We’ve faced a lot of issues over the past few years and I’m sure there are a lot of people who wish it were anyone but Facebook that was helping to propose this.”