Facebook is already under pressure in Washington, where investigators and Congress are examining thousands of Facebook advertisements from the 2016 election. Chief executive Mark Zuckerberg also recently announced plans to sell millions of shares over the next 1½ years for his Chan Zuckerberg Initiative. Its beneficiaries include programs for immigration and prison reform and affordable housing.
Facebook was not immediately available to comment on Trump's tweet.
The company's curation of news articles has drawn ire from both political parties. Last year, Zuckerberg agreed to meet with conservative leaders after accusations that Facebook had suppressed right-leaning news. But Sen. Mark Warner, D-Va., vice chairman of the Senate Intelligence Committee, has also pressed Facebook and other social media companies on accusations they enabled Russian tampering in the U.S. election, calling recent disclosures the "tip of the iceberg."
News organizations, too, have a fraught relationship with the social network. While Facebook and Google offer tools for journalists, a group of news organizations has said the near-duopoly of online advertising is a threat to free press.
Zuckerberg and Trump's relationship has not seen the same public scrutiny as, say, Washington Post owner and Amazon CEO Jeff Bezos. But one of Facebook's most influential investors, Peter Thiel, is a Trump ally. A recent profile in Vanity Fair suggested Thiel is leaning toward more oversight of large technology companies. (Thiel was not immediately available to comment to CNBC).
Nonetheless, Facebook's share price has risen nearly 45 percent so far this year, amid broad gains in the technology industry.
Aside from being avid users of social media, Zuckerberg and Trump have something else in common. Zuckerberg's 2017 tour of America — — has focused on some of the same core issues as Trump's campaign. Zuckerberg has said he hopes to visit 30 states this year because Americans "need to find a way to change the game so it works for everyone."
Correction: This story was revised to correct Sen. Mark Warner's position on the Senate Select Committee on Intelligence. He is vice chairman.