Two associates of Rudy Giuliani tried to recruit a top Ukrainian energy official in March in a proposed takeover of the state oil-and-gas company, describing the company’s chief executive and the then-U.S. Ambassador Marie Yovanovitch as part of “this Soros cartel” working against President Trump.

“You’re a Republican, right?” Andrew Favorov, the head of natural gas for state-run Naftogaz, recalled the men, Lev Parnas and Igor Fruman, asking him, after their reference to investor and Democratic donor George Soros. “We want...