His fixation was only intensified by his hope that he could employ the Ukrainian government to undermine his most prominent potential Democratic rival in 2020, former Vice President Joseph R. Biden Jr.

His personal lawyer, Rudolph W. Giuliani, has undertaken a nearly yearlong, free-ranging effort to unearth information helpful to Mr. Trump and harmful to Mr. Biden.

And Mr. Trump has put the powers of his office behind his agenda: He has dispatched Vice President Mike Pence and top administration officials with thinly veiled messages about heeding his demands about confronting corruption, which Ukrainian and former American officials say is understood as code for the Bidens and Ukrainians who released damaging information about the Trump campaign in 2016. This summer he froze a package of military assistance to Ukraine even as the country, eager to build closer relations with Washington, continued to be menaced by its aggressive neighbor Russia.