"They wanted Twitter, the most important global platform for journalism, to ban me, even though Twitter had repeatedly found my posts did not violate its rules," Berenson alleged. "They wanted to soil my reputation as a reporter and damage me and my family financially."
Berenson said he was going to file a lawsuit against Gottlieb.
On Friday, Gottlieb responded during an interview with CNBC, but said he would not answer to the specific allegation since a lawsuit was pending.
"This is kind of a convoluted conspiracy theory that somehow, you told Twitter to get rid of him because he was asking too many questions about the efficacy and safety of the COVID vaccine. Do you want to respond to that and tell us your side?" asked "'Squawk Box" host Joe Kernen.
"I've raised concerns about social media broadly, and I've done it on these networks around the threats that were being made on these platforms and the inability of these platforms to police direct threats, physical threats about people," Gottlieb explained.
"That's my concerns around social media and what's going on in that ecosystem," he added.
Kernen went on to detail his own experience with the virus and how vaccines kept him from getting severely sick.
"I'm unconcerned about debate," Gottlieb continued. "I'm unconcerned about debate taking place in platforms, I'm very concerned when physical threats are being made, physical threats against people's safety. I'm very concerned about physical threats against people's safety and the people who gin up those threats against individuals, that concerns me."
Gottlieb reiterated the point on his Twitter account.
"Respectful debate and dialogue is one thing, and should be encouraged and protected. But there's no place for targeted harassment, and misleading dialogue which can instigate a small but persuadable group of people to make targeted and dangerous threats," he tweeted.
Berenson said he has sent legal "demand" letters to Gottlieb and Pfizer, and says he has grounds to use them on the basis of a conspiracy to interfere with his civil rights.