(CNN) A lawyer for Rudy Giuliani's indicted associate Lev Parnas said Giuliani directed Parnas to issue an ultimatum earlier this year to a representative of incoming Ukrainian President Volodymyr Zelensky, warning him that if the new government didn't announce an investigation into Joe Biden, the US would freeze military aid and Vice President Mike Pence would not attend Zelensky's inauguration.

Parnas' lawyer Joseph Bondy made the comments to The New York Times, which reported Sunday that Parnas believed Giuliani -- President Donald Trump's personal attorney -- was acting with Trump's authorization and traveled to Kiev to convey the message just prior to Zelensky's inauguration in May. But both Giuliani and the meeting's other participants denied Parnas' account to the Times.

There is no evidence of wrongdoing in Ukraine by either Joe Biden or his son Hunter, who served on the board of a Ukrainian gas company.

The account from Parnas, who along with other Giuliani associate Igor Fruman pleaded not guilty last month to criminal charges that they funneled foreign money into US elections, suggests that he is willing to implicate Trump and Giuliani in the unraveling Ukraine scandal.

Giuliani rebutted Parnas' claim, telling the Times, "Categorically, I did not tell him to say that."

A person familiar with the events told the newspaper the meeting consisted of Parnas, Fruman and Serhiy Shefir, a close aide to Zelensky, drinking coffee at an outdoor cafe days before Zelensky's inauguration.

Fruman, who also attended the meeting, pushed back on Parnas' account. Fruman's lawyer John Dowd told the Times that the men looked only to meet with Zelensky and never brought up the US aid or Pence's presence at the inauguration.

CNN has reached out to Giuliani and representatives for Parnas and Fruman for comment.

Shefir told the Times in a statement that he met with Parnas and Fruman. He noted that Parnas and Fruman did not bring up military aid and had asked for a meeting between Zelensky and Giuliani.

"We did not treat Mr. Parnas and Mr. Fruman as official representatives, and therefore we did not consider that they could speak on behalf of the U.S. government," Shefir said in a statement to the Times.

In the end, Pence did not attend Zelensky's inauguration -- a move that a whistleblower complaint later asserted came at the direction of Trump. Pence's office told the Times that it had communicated to Ukrainian officials that Pence would not attend a week before the inauguration on May 13. The $400 million in military and security assistance to Ukraine was frozen, though it remains unclear whether that was connected to this alleged threat, and it was released in early September.