Mr. Giuliani, the president’s personal lawyer, met in Budapest on Tuesday with a former Ukrainian prosecutor, Yuriy Lutsenko, who has become a key figure in the impeachment inquiry. He then traveled to Kyiv on Wednesday seeking to meet with other former Ukrainian prosecutors whose claims have been embraced by Republicans, including Viktor Shokin and Kostiantyn H. Kulyk, according to people familiar with the effort…

Mr. Giuliani is using the trip, which has not been previously reported, to help prepare more episodes of a documentary series for a conservative television outlet promoting his pro-Trump, anti-impeachment narrative. His latest moves to advance the theories propounded by the prosecutors amount to an audacious effort to give the president’s supporters new material to undercut the House impeachment proceedings and an eventual Senate trial.

It was Mr. Giuliani’s earlier interactions with some of the same Ukrainian characters that set the stage for the impeachment inquiry in the first place, and also led to an investigation by federal prosecutors into whether Mr. Giuliani violated federal lobbying laws.