Facebook CEO Mark Zuckerberg smiles at South Bend Mayor Pete Buttigieg after being asked about Buttigieg as a politician as they walk into the St. Joseph County Juvenile Justice Center during a surprise visit to South Bend, Ind., Saturday, April 29, 2017.

Facebook CEO Mark Zuckerberg has too much power, Democratic presidential candidate Pete Buttigieg told The New York Times in an interview published Thursday.

"No one should have that kind of power," Buttigieg told the Times editorial board.

Buttigieg told the Times that just because he and Zuckerberg share friends and both went to Harvard University "doesn't mean we agree on a lot of things." Buttigieg advocated for "a standard that shifts the burden to large companies, especially when they're making acquisitions, like the acquisition of WhatsApp by Facebook, that are likely anti-competitive."

He also criticized Facebook's advertising policy that allows politicians to run false ads without fact-checks.

"There's a problem of their refusal to accept their responsibility for speech that they make money from," Buttigieg told the Times. "So, if a cable company, or a newspaper, if somebody can show that an ad that you all were going to run is false, you would pull it, and yet Facebook doesn't want to hold themselves to that same standard."

Previous reports have painted a fairly friendly relationship between Zuckerberg and the former mayor of South Bend, Indiana. A Buttigieg campaign spokesperson confirmed an October Bloomberg report that Zuckerberg and his wife, Priscilla Chan, successfully recommended two people to be hired to the campaign. Buttigieg and Zuckerberg overlapped at Harvard and were later connected through a mutual friend, according to Bloomberg.

For all his criticism of tech, Buttigieg has remained a popular candidate in Silicon Valley. While his approach is far more tempered than that of Massachusetts Sen. Elizabeth Warren, who outwardly advocates breaking up Big Tech, Buttigieg told the Times he believes "there's a strong case" for doing so at Facebook.

He said many Silicon Valley tech workers support him even though they may disagree with some of his positions.

"I think you got a lot of folks there who are maybe a little less ideological, who I'm not going to agree with on everything, but also a lot of folks who, I think, are wrestling with what it is they've created," Buttigieg said.

Facebook did not immediately respond to CNBC's request for comment.

Read the full interview at The New York Times.

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