Messrs. Trump and Giuliani have suggested that Joe Biden pushed for the firing of Ukraine’s general prosecutor, Viktor Shokin, in March 2016 to stop an investigation into Burisma. In Ukraine, government officials and anticorruption advocates say that is a misrepresentation. Neither Mr. Biden nor his son have been accused of any wrongdoing.

Mr. Biden had called for the ouster of Mr. Shokin because he and others thought that the prosecutor wasn’t aggressive enough.

The owner of Burisma, Mykola Zlochevsky, has been under the scrutiny of prosecutors. A minister of natural resources until 2012, Mr. Zlochevsky was accused of improperly granting gas extraction licenses to firms affiliated with him, and at times was investigated for alleged abuse of power, illegal enrichment and money laundering. Mr. Zlochevsky was never convicted of any crimes and denied any wrongdoing. His lawyer also denied that Mr. Zlochevsky ever benefited from his position in government.

Mr. Shokin had dragged his feet on those investigations, Western diplomats said, and effectively squashed one in London by failing to cooperate with U.K. authorities, who had frozen $23.5 million of Mr. Zlochevsky’s assets.