The emails indicate that Mr. Pompeo spoke at least twice by telephone with Mr. Giuliani in March as Mr. Giuliani was urging Ukraine to investigate Mr. Trump’s rivals, and trying to oust a respected American ambassador to Ukraine, Marie L. Yovanovitch, who had been promoting anticorruption efforts in the country. Mr. Pompeo ordered Ms. Yovanovitch’s removal the next month. The first call between Mr. Giuliani and Mr. Pompeo was arranged with guidance from Mr. Trump’s personal assistant, the documents suggest.

The documents also show that the State Department sent members of Congress a deliberately misleading reply about Ms. Yovanovitch’s departure after they asked about pressure on her. As part of the effort to oust her, Mr. Giuliani and his associates encouraged news outlets favorable to the president to publicize unsubstantiated claims about Ms. Yovanovitch’s disloyalty to Mr. Trump.

The documents, and recent congressional testimonies in the impeachment inquiry, tie Mr. Pompeo closely to efforts by Mr. Trump and Mr. Giuliani to persuade the Ukrainian government to announce investigations that could help Mr. Trump politically.