"Professional journalists don’t go on national television and make up allegations, even against their critics," Media Matters chairman David Brock wrote to Attkisson in an email provided to TPM.
Attkisson said during an appearance Sunday on CNN that Media Matters may have been paid to go after her.
She told CNN's Brian Stelter that she had received help from Media Matters until she began to report on "Fast & Furious" and other stories that were unflattering to the Obama administration.
Attkisson left CBS last month, reportedly citing her concern that the network was liberally biased.
A spokesperson for Media Matters promptly denied the charge that the group was paid to target her, and Brock wrote in his email that it's "completely unfathomable" that Attkisson made the claim "without a shred of evidence."
"If you have such evidence to show that Media Matters was paid to target you, I ask that you publicly release it," Brock wrote. "If you have no evidence to back up your charge, I ask that you publicly apologize and correct your false claims against us."
A spokeswoman for Media Matters said Attkisson had yet to respond to the email as of Tuesday morning.