NEW YORK, NY - APRIL 16: (L to R) Adult film actress Stormy Daniels (Stephanie Clifford) and Michael Avenatti, attorney for Stormy Daniels, speak to the media as they exit the United States District Court Southern District of New York for a hearing related to Michael Cohen, President Trump's longtime personal attorney and confidante, April 16, 2018 in New York City.  Cohen and lawyers representing President Trump are asking the court to block Justice Department officials from reading documents and materials related to Cohen's relationship with President Trump that they believe should be protected by attorney-client privilege. Officials with the FBI, armed with a search warrant, raided Cohen's office and two private residences last week.  (Photo by Drew Angerer/Getty Images)
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NEW YORK, NY - APRIL 16: (L to R) Adult film actress Stormy Daniels (Stephanie Clifford) and Michael Avenatti, attorney for Stormy Daniels, speak to the media as they exit the United States District Court Southern District of New York for a hearing related to Michael Cohen, President Trump's longtime personal attorney and confidante, April 16, 2018 in New York City. Cohen and lawyers representing President Trump are asking the court to block Justice Department officials from reading documents and materials related to Cohen's relationship with President Trump that they believe should be protected by attorney-client privilege. Officials with the FBI, armed with a search warrant, raided Cohen's office and two private residences last week. (Photo by Drew Angerer/Getty Images)
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(CNN) —  

Lawyers for Michael Cohen, President Donald Trump’s longtime personal attorney, are accusing the lawyer representing porn star Stormy Daniels of circulating false information about Cohen.

In a court filing on Wednesday, Cohen’s attorneys also acknowledged the accuracy of some of the information Michael Avenatti released publicly on Tuesday and suggested that Avenatti obtained that information unlawfully.

Cohen’s filing was the first comment from his side since Avenatti published his own research Tuesday.

“While much of the information in his ‘report’ is completely inaccurate, Mr. Avenatti has published some information that appears to be from Mr. Cohen’s actual bank records, and Mr. Cohen has no reason to believe that Mr. Avenatti is in lawful possession of these records,” Cohen’s attorneys write.

Avenatti shot back Wednesday night on Twitter, saying, “They fail to address, let alone contradict, 99% of the statements in what we released. Among other things, they effectively concede the receipt of the $500,000 from those with Russian ties.”

In a memo posted online Tuesday afternoon, Avenatti alleged that Cohen had received payments after the 2016 election from a company linked to Viktor Vekselberg, a Russian oligarch with close ties to the Kremlin, and from pharmaceutical giant Novartis, Korea Aerospace Industries and telecommunications conglomerate AT&T, among other things.

Cohen’s attorneys argue that Avenatti, in his report, used bank records and information about a Michael Cohen who is a Canadian in Tanzania and another Michael Cohen in Israel. Those transactions amounted to less than $1,000 each, Avenatti said.

But Cohen’s attorneys acknowledge that AT&T and Novartis were the Trump-related Michael Cohen’s clients, and records about those relationships were seized in the April raid of Cohen’s possessions, which he’s now fighting in court. The payments Avenatti alleges Cohen received from corporate entities amounted to hundreds of thousands of dollars from each company.

Avenatti has also alleged that a Russian oligarch “routed eight payments” totaling a half-million dollars to Cohen through a company in the US named Columbus Nova in 2017.

Cohen’s attorneys refer in their court filing Wednesday to the public denial by Columbus Nova. The company has said the Russian oligarch Vekselberg never “had any contractual relationship” with Cohen. Cohen’s attorneys do not provide further details to clarify Cohen’s relationship with Vekselberg, simply calling some of Avenatti’s report a “toxic mix of misinformation.”

Columbus Nova has acknowledged paying Cohen but says Vekelsberg is just an investor and had no role in the decision to pay or the payment to Cohen.

Cohen’s attorneys also allege Avenatti obtained some of the information illegally and ask the judge to make him say how he received it.

Avenatti has commanded wall-to-wall media coverage for his client Daniels, who sued Cohen and Trump in California before a federal judge halted that lawsuit. Avenatti has simultaneously led Daniels’ attempt to intervene in Cohen’s challenge over prosecutor’s criminal investigation of his business dealings.

Because Avenatti is Los Angeles-based, he has to gain permission from the New York court to appear in this matter.

Cohen’s attorneys said Wednesday they are not opposed to Daniels, whose real name is Stephanie Clifford, becoming an additional party in his court case.

Avenatti has remained steadfast in what he’s alleged since Tuesday night.

“They still haven’t told anyone truly what the arrangement was with Michael Cohen, what it was for, why did they hire Michael Cohen to undertake this effort – to this effort and what they haven’t said is that there was absolutely no contacts whatsoever or connection between their entity and this oligarch or Russia,” Avenatti said Tuesday night on CNN.