Mr. Trump’s insistence that he was focused on corruption also lacks support. For one, he did not raise those concerns during his July 25 call with Mr. Zelensky or in an April 21 call. The Pentagon had also certified in May that Ukraine had “taken substantive actions” to root out corruption. The military aid to Ukraine was withheld in July and released on Sept. 11, but neither Mr. Trump nor his aides have specified what corruption improvements had been made in Kyiv in those two months.

What Was Said

“How about the guy with the telephone? How about that one? I guarantee you that never took place.”

This is disputed. David Holmes, the political counselor at the United States Embassy in Ukraine, testified on Thursday that he had overheard a cellphone call between Mr. Trump and Gordon D. Sondland, the United States ambassador to the European Union, in July. During the call, Mr. Holmes said, Mr. Trump had asked Mr. Sondland about Ukrainian investigations into his political rivals. Mr. Holmes testified that he provided an account of the call to his boss immediately afterward and also informed other colleagues at the embassy in Kyiv.

Though Mr. Trump insisted Mr. Holmes’s account was wrong, Mr. Sondland said Wednesday in congressional testimony that he had “no reason” to doubt it, though he could not recall precise details of their conversation.

“It’s true that the president speaks loudly at times, and it’s also true — I think we primarily discussed ASAP Rocky,” Mr. Sondland said, referring to the American rapper who was charged with assault in Sweden around that time.

“Actually, actually, I would have been more surprised if President Trump had not mentioned investigations, particularly given what we were hearing from Mr. Giuliani about the president’s concerns,” he said, referring to Rudolph W. Giuliani, the president’s personal lawyer. “However, I have no recollection of discussing Vice President Biden or his son on that call or after the call ended.”

What Was Said

“This was an Obama person. Wouldn’t — didn’t want to hang my picture in the embassy.”

This lacks evidence. The president was referring to Marie L. Yovanovitch, a career diplomat who served as the United States ambassador to Ukraine until he recalled her this spring. She had come under intense criticism from allies of Mr. Trump, including Mr. Giuliani and Donald Trump Jr., who helped spread accusations that Ms. Yovanovitch was insufficiently loyal to the president. She has become a witness in the impeachment inquiry.

Mr. Trump’s remark about his portrait may have been drawn from an exchange between Representative Lee M. Zeldin, Republican of New York, and Mr. Holmes during closed congressional testimony last week.