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Rudy Giuliani's expected appearance before January 6 committee canceled but talks continue, his lawyer says

(CNN) Rudy Giuliani's appearance before the January 6 committee, set for Friday, has been canceled, his attorney told CNN.

Robert Costello said his client had been expected to appear virtually before the panel on Friday. On Thursday, Giuliani asked to record the interview, both audio and video, but the committee rejected that request, Costello said.

Although Friday's meeting is off, Costello said, talks between the two sides continue.

Tim Mulvey, January 6 House select committee spokesperson, said Thursday in a statement that Giuliani recording the interview "was never an agreed-upon condition."

Mulvey said Giuliani remains under subpoena as "an important witness to the conspiracy to overthrow the government."

"If he refuses to comply the committee will consider all enforcement options," Mulvey said.

The now-canceled appearance was to have followed months of negotiations between lawmakers and the former mayor of New York, who served as former President Donald Trump's personal attorney for much of his presidency.

A central figure in Trump's failed bid to overturn the 2020 election, Giuliani was subpoenaed by the committee in January and has been engaging with lawmakers, through his lawyer, about the scope of the subpoena and whether he may be able to comply with some requests.

In its subpoena, the committee alleges that Giuliani "actively promoted claims of election fraud on behalf of the former President and sought to convince state legislators to take steps to overturn the election results." The subpoena also states that Giuliani was in contact with Trump and members of Congress "regarding strategies for delaying or overturning the results of the 2020 election."

As with other witnesses under subpoena, the committee has previously said it expects Giuliani to "cooperate fully."

Several high-profile individuals from Trump's inner orbit have recently spoken with the committee voluntarily. Donald Trump Jr. met with the committee on Tuesday. Trump's daughter and former senior White House adviser, Ivanka Trump, was interviewed for nearly eight hours last month, and her husband, Jared Kushner, has met with the panel as well.

Giuliani also faces legal woes on several other fronts. CNN has reported that federal prosecutors in New York may soon reach a charging decision regarding his foreign lobbying efforts involving Ukraine. He faces possible fines or settlements for his actions trying to overturn the 2020 election results to favor Trump. And Dominion Voting Systems has filed a billion-dollar defamation lawsuit against him for his unfounded election fraud claims.

This story has been updated with additional developments Thursday and details.

CNN's Ryan Nobles contributed to this report.