Democratic presidential candidate Pete Buttigieg told CBS News on Thursday that he believes Facebook's advertisement policy is "a mistake" and that the breakup of big technology companies is a "remedy that should be on the table."

The mayor of South Bend, Indiana, called for greater accountability on the part of the social media giant, which has come under scrutiny in recent weeks.

"[Facebook] has a responsibility to pull false advertising," Buttigieg said. "And yes, they also have a responsibility to intervene when there is advertising that will contribute to voter suppression."

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The candidate's remarks come a day after Facebook founder and CEO Mark Zuckerberg was grilled by the House Financial Services Committee in a marathon hearing. Congresswoman Maxine Waters, the Democratic committee chairwoman from California, told Zuckerberg, "The impact of this will be a massive voter suppression effort. Your claim to promote freedom of speech does not ring true."

Earlier this month, Facebook denied requests from former Vice President Joe Biden's campaign to remove a misleading video about Biden from President Trump's re-election campaign. Biden spokesperson TJ Ducklo said there is "no excuse for companies like Facebook to refuse to do the right thing." He added, "Our very democracy is at stake in 2020, and we must do better than this."

Buttigieg also told reporters on Thursday that the breakup of big tech companies like Facebook is a "remedy that should be on the table," along with fines.

However, he said such anti-trust breakups should not be "declared in advance by a politician." That's a swipe at his opponent Senator Elizabeth Warren, who recently became the Democratic frontrunner and released a regulatory plan in March to break up tech giants like Facebook, Amazon and Google.

Zuckerberg admitted to employees earlier this month that a Warren presidency could "suck" for the company, according to leaked audio published by The Verge.

"If she gets elected president, then I would bet that we will have a legal challenge, and I would bet that we will win the legal challenge. And does that still suck for us? Yeah," Zuckerberg reportedly said. "But look, at the end of the day, if someone's going to try to threaten something that existential, you go to the mat and you fight."

In a separate incident involving both Facebook and the Buttigieg campaign, Zuckerberg confirmed to CBS News that he and his wife recommended two of their colleagues to work on the candidate's presidential campaign.

"This shouldn't be taken as an endorsement. We have several mutual friends in college who introduced [us]" several years ago, Zuckerberg said during a conference call. Buttigieg and Zuckerberg both attended Harvard University.