After a closed-door meeting at the company's Silicon Valley headquarters, Zuckerberg defended his company's practices but acknowledged that many conservatives believe Facebook is politically liberal.
"It doesn't make sense for our mission or our business to suppress political content," Zuckerberg wrote on Facebook after the meeting.
"I know many conservatives don't trust that our platform surfaces content without a political bias," he added. "I wanted to hear their concerns personally and have an open conversation about how we can build trust. "
The editorial practices at the world's largest social network came under scrutiny after a former Facebook contractor anonymously accused editors there of deliberately suppressing conservative news. The allegations were reported by technology news website Gizmodo, which did not identify the ex-contractor.
Facebook has denied the allegations and said it would conduct a full investigation.
A Facebook spokeswoman said the meeting produced "a constructive discussion" and some attendees called it productive.
"I think Facebook is very sincere in wanting to resolve outstanding issues with conservatives," Brent Bozell, president of the Media Research Center, said after the meeting.
Attendees were frank about their concerns, but the tone was cordial, Bozell said. "Facebook invited that frank talk. People didn't hold back too much," he said.
On her Facebook page, conservative CNN commentator S.E. Cupp said the meeting had produced "strong commitments to address issues, as well as to work together on common goals."
Other attendees included former White House press secretary Dana Perino, media personality Glenn Beck and former Republican Senator Jim DeMint.
Zuckerberg said that while Silicon Valley has a reputation for being liberal, Facebook's 1.6 billion users span every background and ideology.
"The reality is, conservatives and Republicans have always been an important part of Facebook," Zuckerberg wrote.
Presumptive Republican nominee Donald Trump has more Facebook fans than any other presidential candidate, he said. Fox News "drives more interactions on its Facebook page than any other news outlet in the world," Zuckerberg added. "It's not even close."
Fox News is owned by Rupert Murdoch's 21st Century Fox.
Facebook employees who donate to presidential candidates lean Democratic. Seventy-nine percent of employee contributions to 2016 contenders went to Democrats, according to a Reuters analysis of campaign finance data, and 21 percent to Republicans.
Zuckerberg has contributed to candidates in both parties. Sixty-percent of his donations during the 2014 midterm elections went to Republicans and 40 percent to Democrats. He has not supported a presidential candidate this cycle.
Although a US Senate committee is investigating whether there is liberal bias in selection of trending topics, there is little chance the government will try to regulate Facebook's practices, said Republican Senator John Thune, chairman of the Senate Commerce Committee.
"I don't have any reason to believe that would be necessary," Thune told reporters on Tuesday.
Thune sent a letter to Facebook last week to demand that it explain its editorial decision-making and how stories are chosen for the "trending topics" feature. He said his primary concern was that Facebook was potentially being deceptive about how its news feed curation algorithms work.
Facebook last week released its guidelines for choosing trending topics, but the operations of the news feed algorithm remain closely guarded.
Legal experts said the government has few tools to dictate how a private company makes news decisions.
"As a legal matter, Facebook is not required to be even-handed," said Eugene Volokh, a law professor at the University of California, Los Angeles. "Congress can't introduce something that tries to prohibit Facebook from making these kinds of choices."
© Thomson Reuters 2016
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