Rudy Giuliani, former mayor of New York Anthony Behar | Bloomberg | Getty Images

President Donald Trump's personal attorney Rudy Giuliani met in Europe this week with a former Ukrainian prosecutor and other officials, even as a House committee pushed forward an impeachment inquiry focused on Trump and Giuliani's pressuring of Ukraine, a new report said. Giuliani met Tuesday with a former Ukrainian prosecutor, Yuriy Lutsenko, in Budapest, The New York Times reported, citing people familiar with the matter. On Wednesday, Giuliani traveled to Kyiv, Ukraine's capital, hoping to meet with other ex-Ukrainian prosecutors, including Viktor Shokin and Kostiantyn Kulyk, the Times reported. Giuliani reportedly is also helping right-wing news network One America News produce episodes of a documentary series promoting his arguments against Democrats' impeachment inquiry in the House.

He was accompanied in Budapest by a crew from that network, including a reporter who interviewed Lutsenko there, a person familiar with the situation told the Times. Giuliani in the past year coordinated with Trump administration officials as part of a campaign to get Ukrainian President Volodymyr Zelenskiy to announce investigations into Burisma Holdings, a Ukrainian gas company where former Vice President Joe Biden's son Hunter previously served as a board member. As vice president, Biden called on Ukraine to oust Shokin as prosecutor general — an effort that has led some critics to accuse him of intervening to protect his son. But Biden's actions were consistent with U.S. foreign policy at the time. House Democrats are investigating whether Trump abused his power by pressuring Ukraine to announce that probe of Burisma, as well as an inquiry involving a debunked conspiracy theory that Ukraine meddled in the 2016 U.S. presidential election, to help his own reelection in 2020. Giuliani and some of Trump's allies have seized upon some of the claims made by the former Ukrainian prosecutors, such as Shokin, who had said that his firing was related to a probe of Burisma. Giuliani did not immediately respond to CNBC's request for comment on the Times' story. But prior to its publication, Giuliani sent NBC News a lengthy text message slamming a 300-page report released Tuesday by Democrat-led House committees, which goes into detail about the evidence of alleged wrongdoing by Trump.