"Mr. Cohen inexplicably accepted these payments while he was the personal attorney to the President and holding himself out at times as employed by the Trump Organization," Avenatti's report said.
"This was occurring at the same time significant questions were being raised relating to (a) the involvement of Russia and Vladimir Putin in the 2016 Presidential Election and (b) the extent of the relationship between Mr. Putin and Mr. Trump."
The report noted that Columbus Nova is a private equity firm founded in 2000 with more than $2 billion in assets.
An attorney for Columbus Nova said in a statement that the "claim that Viktor Vekselberg was involved in or provided any funding for Columbus Nova's engagement of Michael Cohen is patently untrue." Here's the full statement from the firm's attorney:
Columbus Nova is an investment management company solely owned and controlled by Americans. After the inauguration, the firm hired Michael Cohen as a business consultant regarding potential sources of capital and potential investments in real estate and other ventures. Reports today that Viktor Vekselberg used Columbus Nova as a conduit for payments to Michael Cohen are false. The claim that Viktor Vekselberg was involved in or provided any funding for Columbus Nova's engagement of Michael Cohen is patently untrue. Neither Viktor Vekselberg nor anyone else outside of Columbus Nova was involved in the decision to hire Cohen or provided funding for his engagement.
Additionally, contrary to recent reports, Columbus Nova LLC and Renova U.S. Management, LLC (operated under the Columbus Nova umbrella) are not now, nor have ever been, owned by any foreign entity or person. In fact, since its founding nearly 20 years ago, Columbus Nova has been and continues to be 100% owned by Americans.
As reported in May 2018 by The New York Times, the Renova Group is Columbus Nova's biggest client. When Columbus Nova formed a management company under the name Renova U.S. Management, its largest client at the time was a Renova Group company. Throughout its existence, Columbus Nova has managed assets on behalf of Renova Group companies and other clients. Columbus Nova itself is not now, and has never been, owned by any foreign entity or person including Viktor Vekselberg or the Renova Group. The same is true with regard to all investment management companies under the Columbus Nova umbrella.
Avenatti also claimed that drug giant Novartis in late 2017 and early 2018 made four separate payments totaling nearly $400,000 to Cohen's company, shortly before Trump had a dinner meeting with the incoming CEO of Novartis.
A report prepared by Avenatti's law firm also said Cohen's company, Essential Consultants, "received $200,000 in four separate payments of $50,000 in late 2017 and early 2018 from AT&T."
A Novartis spokesperson said in a statement that "any agreements with Essential Consultants were entered before our current CEO taking office in February of this year and have expired."
AT&T on Tuesday evening confirmed that it paid Cohen for "insights" into the presidential administration.
In a prepared statement, AT&T told CNBC that Cohen's firm "was one of several firms we engaged in early 2017 to provide insights into understanding the new administration. They did no legal or lobbying work for us, and the contract ended in December 2017."
Avenatti's report also claimed that "Essential also received a $150,000 payment in November 2017 from Korea Aerospace Industries LTD."
Cohen and Avenatti did not immediately respond to a request for comment.
Last week, The New York Times reported that federal agents working for Mueller stopped Vekselberg at a New York-area airport several months ago and questioned him, in addition to searching electronic devices.
Mueller is investigating Russian interference in the election, as well as possible collusion by the Trump campaign in that effort.
Vekselberg has not been identified as a suspect or charged in connection with any investigation of Cohen.
In addition to Mueller's probe, Cohen is under criminal investigation by federal prosecutors in New York who are eyeing his business dealings, including the hush-money payoff to Daniels.
The bombshell claim by Avenatti is just the latest in a series of explosive charges he has made against Cohen and Trump since taking Daniels' case earlier this year. She is suing both Cohen and Trump seeking to be released from a non-disclosure agreement.
Cohen has admitted paying Daniels, whose real name is Stephanie Clifford, the $130,000 in exchange for her agreement not to publicly discuss an affair she claims to have had with Trump in 2006.
The White House has denied the affair. Last week, Trump's new lawyer, former New York City mayor Rudy Giuliani, said the president had reimbursed Cohen for the payments to Daniels.