In conversations in the first months of the year with the president, Mr. Giuliani, by his account, cast Ms. Yovanovitch as impeding not only investigations in Ukraine that could benefit Mr. Trump, but also Mr. Giuliani’s efforts to gather evidence to defend him — and target his rivals — in the United States.

“There’s a lot of reasons to move her,” Mr. Giuliani said, asserting that his briefings of Mr. Trump and Mr. Pompeo most likely played a role in their decision to recall Ms. Yovanovitch.

“I think my information did,” he said. “I don’t know. You’d have to ask them. But they relied on it.”

He added that he did not recommend that Mr. Trump or Mr. Pompeo recall Ms. Yovanovitch. “I just gave them the facts,” he said. “I mean, did I think she should be recalled? I thought she should have been fired.” He said, “If I was attorney general, I would have kicked her out. I mean — secretary of state.”