Sen. Rand Paul Randal (Rand) Howard PaulRand Paul says he can't judge 'guilt or innocence' in Breonna Taylor case Overnight Health Care: Health officials tell public to trust in science | Despair at CDC under Trump influence | A new vaccine phase 3 trial starts Health officials tell public to trust in science MORE (R-Ky.) said Thursday that Facebook must convince conservatives they are not censoring them if it wants to keep making money.

"I think if it gets so bad that they don't allow conservative viewpoints on Facebook, I think you will get to a point where people will leave in droves," Paul told CNN Thursday.

"So Facebook, if they want to keep making money, are going to have to convince conservatives that they're not the enemy."

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Many on the right have criticized Facebook and other online platforms, accusing them of censoring conservative voices. In July, lawmakers on the House Judiciary Committee also held a hearing to look into the issue.

Facebook and other companies have denied they are biased against conservatives. But some at the company have also cricized what they see as a "political monoculture."

On Sunday, The Wall Street Journal reported that a former top executive at the company, Palmer Luckey, said he was ousted for donating to a group that funded attack ads against Hillary Clinton Hillary Diane Rodham ClintonDemocratic groups using Bloomberg money to launch M in Spanish language ads in Florida The Hill's Campaign Report: Presidential polls tighten weeks out from Election Day More than 50 Latino faith leaders endorse Biden MORE.

In May, Facebook hired outside advisers to help it detect and address racial biases in its ad placements and any targeting of conservative viewpoints.

Paul said Thursday that the issue "presents a conundrum" for conservatives.

"It's a privately owned company," he said. "Most times, conservatives, we don't want to over-regulate private businesses.

"But they do have sort of a monopoly on this sort of social exchange in speech," he added.

Some have floated tighter regulation of Facebook, while others say users will just leave for other platforms. Paul said he thinks "people already are" seeking alternative platforms.

"[W]hat I've been saying for a while is that we need to look at the barriers to entry that government might be creating," Paul told CNN.

"Not the government starting other companies but the government getting out ... to allow competition with Facebook."