WASHINGTON — When Rudolph W. Giuliani set out to dredge up damaging information on President Trump’s rivals in Ukraine, he turned to a native of the former Soviet republic with whom he already had a lucrative business relationship.

Lev Parnas, a Ukrainian-American businessman with a trail of debts and lawsuits, had known Mr. Giuliani casually for years through Republican political circles. Last year, their relationship deepened when a company he helped found retained Mr. Giuliani — associates of Mr. Parnas said he told them he paid hundreds of thousands of dollars — for what Mr. Giuliani said on Thursday was business and legal advice.

Even as he worked with Mr. Parnas’s company, Fraud Guarantee, Mr. Giuliani increasingly relied on Mr. Parnas to carry out Mr. Trump’s quest for evidence in Ukraine that would undercut the legitimacy of the special counsel’s investigation into Russia’s interference on his behalf in the 2016 election and help him heading into his 2020 re-election campaign.

Mr. Giuliani dispatched Mr. Parnas and an associate, Igor Fruman, a Belarusian-American businessman, to Kiev, the Ukrainian capital, where, despite fending off creditors at home, BuzzFeed reported, they ran up big charges at a strip club and the Hilton International hotel. Their mission was to find people and information that could be used to undermine the special counsel’s investigation, and also to damage former Vice President Joseph R. Biden Jr., a prospective Democratic challenger to Mr. Trump.