WASHINGTON—Energy Secretary Rick Perry said he sought out Rudy Giuliani this spring at President Trump’s direction to address Mr. Trump’s concerns about alleged Ukrainian corruption, a sign of how closely the president’s personal lawyer worked with the administration on Ukraine policy.

Mr. Perry, in an exclusive interview with The Wall Street Journal, said he contacted Mr. Giuliani in an effort to ease a path to a meeting between Mr. Trump and his new Ukrainian counterpart. He said Mr. Giuliani described to him during their...