This month, Ms. Warren’s campaign also sent an email seeking donations with the subject line “re: Mark Zuckerberg.” And at a rally in San Diego, as she talked about the power of huge corporations, she told the crowd, “Break them up. And yes, Mark Zuckerberg, I’m looking at you.”

For Facebook, the situation is tricky. The social media company has struggled in recent years with what to allow and disallow on its site, especially after revelations that Russian operatives used the platform during the 2016 presidential election to post disinformation to inflame the American electorate. Facebook has moved to clamp down on false content. Yet when the company removes or buries messages, ads, photos and videos, it is often called out for bias and censorship. Facebook has faced particular wrath from conservatives, who have said the social network intentionally suppresses what they say.

“Facebook believes political speech should be protected,” a spokesman for Facebook said on Saturday. “If Senator Warren wants to say things she knows to be untrue, we believe Facebook should not be in the position of censoring that speech.”

Truth in social media advertising is likely to become a bigger issue ahead of the 2020 presidential election. Mr. Zuckerberg is scheduled to speak about Facebook’s political speech policies this coming week at Georgetown University.

Presidential candidates have been spending huge sums on ads on Facebook and other social media platforms to reach voters. Some campaigns have focused on advertising specifically on Facebook given its sheer size — it has more than 2.2 billion users worldwide — and the ability to spread ads and content cheaply and quickly across the platform.