WASHINGTON — More than two years ago, Pavel Fuks, a wealthy Ukrainian-Russian developer looking for ways to attract more investment from the United States to his hometown, Kharkiv, Ukraine, enlisted an especially well-connected American to help him: Rudolph W. Giuliani.

Mr. Fuks, who years earlier had discussed a Moscow tower project with Donald J. Trump, hired Mr. Giuliani, who in 2018 would become the president’s personal lawyer, under a one-year deal to help improve Kharkiv’s emergency services and bolster its image as a destination for investment.

“I would call him the lobbyist for Kharkiv and Ukraine — this is stated in the contract,” Mr. Fuks said in an interview in March for an episode of The New York Times’s television show, “The Weekly.” Mr. Fuks added: “It is very important for me that such person as Giuliani tells people that we are a good country, that people can do business with us. That’s what we would like to bring to America’s leaders.”