Mr. Perry also said he never heard the president, any of his appointees, Mr. Giuliani or the Ukrainian regime discuss the possibility of specifically investigating former Vice President Joe Biden, a Democratic presidential contender, and his son Hunter Biden. Mr. Trump’s request for a probe of the Bidens in a July 25 call with Ukraine’s president has sparked the impeachment inquiry in the House…

Mr. Perry’s phone call to Mr. Giuliani came after a May meeting at the White House following the inauguration of the Ukrainian president. U.S. officials at that meeting, including Mr. Perry and Kurt Volker, the U.S. envoy for Ukraine negotiations, urged Mr. Trump to meet his new counterpart. Mr. Trump told officials there that they needed to work with Mr. Giuliani to resolve his concerns before he would agree to such a meeting, according to people familiar with the matter.

Mr. Trump said he wasn’t comfortable that the Ukrainians had “straightened up their act,” a concern that Mr. Perry later understood to be related to Mr. Trump’s 2016 campaign, Mr. Perry said, quoting Mr. Trump. “Visit with Rudy,” Mr. Perry said the president told him.