Dana Perino, co-host of Fox News Channel’s “The Five,” says that Facebook recognizes that it has a ‘trust problem’ with conservatives following her meeting Wednesday with the social network’s CEO Mark Zuckerberg.

Perino, former White House press secretary for President George W. Bush, was among a group of leading conservatives invited to the meeting at Facebook’s headquarters in Menlo Park, Calif., following a Gizmodo report that stories about conservative topics were prevented from appearing in Facebook’s trending module. “FOX & Friends Weekend” co-host and Daily Caller founder Tucker Carlson also attended the meeting.

“They acknowledged that they have a trust problem with a significant portion of their customer base and that they were trying to figure out a way, at least a first step, to open a dialogue so that they can try to fix it in the long run,” said Perino, speaking on “The Kelly File” following the meeting.

Among others who attended the special meeting, according to Facebook, were radio host Glenn Beck, American Enterprise Institute President Arthur Brooks, Tea Party Patriots CEO Jenny Beth Martin and Brent Bozell, president of the Media Research Center.

Related: Facebook's CEO Mark Zuckerberg meets with conservatives on reported bias

Perino told Megyn Kelly that there were lots of concerns raised during the meeting that had nothing to do with the particular issue of Trending Topics, noting that the module is a relatively new part of Facebook’s business. “There were lots of concerns raised about their policy on community standards – who gets blocked and for what,” she told Megyn Kelly. “We were kind of pushing on an open door because they recognize that they have a problem and it’s based on trust.”

In a Facebook post afterward, Zuckerberg did not directly respond to allegations that Facebook employees suppressed conservative stories on its "trending topics" feature. But he said, "I know many conservatives don't trust that our platform surfaces content without a political bias."

"I wanted to hear their concerns personally and have an open conversation about how we can build trust. I want to do everything I can to make sure our teams uphold the integrity of our products," he wrote.

In his post, Zuckerberg also noted that Fox News drives more interactions on its Facebook page than any other news outlet in the world. "It's not even close," he added.

Related: Facebook says there is 'no evidence' of anti-conservative bias on Trending Topics

In the meeting, Facebook maintained that it does not have any “direct specific evidence” that conservative news was suppressed on Trending Topics, according to Perino.

The Fox News host said that she found the Facebook executives at the meeting to be “pretty genuine and sincere.”

S.E. Cupp, a columnist with the New York Daily News who attended the meeting, said Zuckerberg, Chief Operating Officer Sheryl Sandberg, Vice President Joel Kaplan and board member Peter Thiel mostly listened to the 17 conservatives who attended.

Speaking on the “The Kelly File,” Carlson said that conservative comments at the meeting “ran the gamut.”

Related: Government requests for Facebook data on the rise, report says

“The problem is that conservatives don’t believe in the type of action that would force a business to comply,” he added.

Not every conservative figure invited to the Facebook meeting attended. American Conservative Union Chairman Matt Schlapp declined the invitation. In a statement, Schlapp said that the "deck is stacked" against conservative opinion at Facebook, adding that CPAC content "egregiously underperforms" on Facebook compared to Twitter and other platforms by factors of 10.

The trending section, which appears to the right of the Facebook news feed, was introduced in January 2014. Facebook describes the module as a product “designed to surface interesting and relevant conversations in order to help you discover the best content from all across Facebook.”

Follow James Rogers on Twitter @jamesjrogers

The Associated Press contributed to this report.