Republican presidential candidate Nikki Haley was asked to explain her earlier remarks about social media companies on Wednesday and said that while she didn't mind "anonymous American" free speech, she didn't support anonymous free speech for actors in Russia, Iran and China.

During an appearance on Fox News on Tuesday, Haley said every person on social media should be "verified by their name." Haley, who was fiercely criticized by fellow Republican candidates for the idea, joined the hosts of CNBC's "Squawk Box" on Wednesday and was asked to explain her comments after "heads exploded." 

Haley said again she wanted social media companies to be transparent with Americans and show their algorithms. 

"What I know, what anyone in intelligence [knows]… Russia, Iran and China, North Korea too, know that the cheapest form of warfare is to spread misinformation. Look at what happened with Israel. You want to know where all this pro-Hamas information is coming from? It is coming from foreign actors that are sowing chaos and division," she said. 

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"I want freedom of speech for Americans. I don’t want freedom of speech for Russia and Hamas, and that’s what’s happening right now. So the way you fix that is we need our social media companies to verify everybody," she said. 

CNBC host Joe Kernen interjected and suggested that she wasn't really saying people can't tweet or post to social media anonymously. Haley said that she believed life would be more "civil" if they were "able to do that," but said people should stand by what they say online. 

"I don’t mind anonymous American people having free speech. What I don’t like is anonymous Russians and Chinese and Iranians having free speech," she said. 

On Tuesday, Haley said everyone on social media should be verified by name.

"When I get into office, the first thing we have to do, social media accounts, social media companies, they have to show America their algorithms. Let us see why they're pushing what they're pushing. The second thing is every person on social media should be verified by their name," Haley said on Fox News.

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Haley described it as a national security threat, and took heat from fellow Republican candidates, Gov. Ron DeSantis, R-Fla., and Vivek Ramaswamy. 

"When you do that, all of a sudden people have to stand by what they say. And it gets rid of the Russian bots, the Iranian bots and the Chinese bots. And then you're going to get some civility when people know their name is next to what they say, and they know their pastor and their family members are going to see it," she said.

DeSantis called Haley's proposal dangerous and said it would be dead on arrival in his administration.

"You know who were anonymous writers back in the day? Alexander Hamilton, John Jay, and James Madison when they wrote the Federalist Papers. They were not ‘national security threats,’ nor are the many conservative Americans across the country who exercise their Constitutional right to voice their opinions without fear of being harassed or canceled by the school they go to or the company they work for," DeSantis wrote on social media. 

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