Zuckerberg proposed the meeting after technology news outlet Gizmodo last week reported allegations that Facebook was deliberately omitting articles with conservative viewpoints from a sidebar that lists popular stories.
Facebook has denied the allegations, reportedly made by a former employee.
In a Facebook post last week, Zuckerberg said he had launched a "full investigation" but no evidence had been found to back up the allegations.
"We have rigorous guidelines that do not permit the prioritization of one viewpoint over another or the suppression of political perspectives," he wrote.
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In an interview with Fox News yesterday, Perino said she believed Facebook was taking the allegations seriously.
"I also think it is probably fairly solvable. So I am looking forward to going tomorrow to hear more about what they found," she said.
Others invited included Zac Moffatt, a political consultant who worked for former Republican presidential candidate Mitt Romney; Arthur Brooks, president of the American Enterprise Institute; and Barry Bennett, an advisor to presumptive Republican presidential candidate Donald Trump.
Not all conservatives accepted the invitation, however.
American Conservative Union chairman Matt Schlapp said Facebook had a history of agitating against conservatives, alleging that his group's content "egregiously underperforms" on Facebook when compared to Twitter and other platforms.
"We will not be attending this meeting. We know one meeting cannot possibly resolve all of the above mentioned issues," Schlapp said in a statement yesterday.
The debate comes with Facebook and other social networks playing a growing role in how people get their news, prompting concern over whether this information is promoted or filtered by online services and applications.