Mr. Trump raised this possibility in his July 25 phone call with the new Ukrainian president, Volodymyr Zelensky. It was not the first time he had cast doubt on Russia’s involvement: In a call to a New York Times reporter moments after meeting Mr. Putin for the first time in Hamburg, Germany, in 2017, Mr. Trump endorsed Mr. Putin’s view that Russia is so good at cyberoperations that it would have never been caught. “That makes sense, doesn’t it?” he asked.

He expressed doubts again in 2018, in a news conference with Mr. Putin in Helsinki, Finland. That was only days after the Justice Department indicted a dozen Russian intelligence officers for their role in the hack; the administration will not say if it now believes that indictment was flawed because there is evidence that Ukranians were responsible.

Whether or not he believes Ukraine was involved, Mr. Giuliani certainly understood the risks of talking on open lines, particularly in a country with an active cyberwar. As a former prosecutor, he knows what the United States and its adversaries can intercept. In more recent years, he has spoken around the world on cybersecurity challenges. And as the president’s lawyer, he was a clear target.

Mr. Giuliani said in a phone interview Monday that nothing he talked about on the phone or in texts was classified. “All of my conversations, I can say uniformly, were on an unclassified basis,” he said.

His findings about what happened in Ukraine were “generated from my own investigations” and had nothing to do with the United States government, he said, until he was asked to talk with Kurt D. Volker, then the special envoy for Ukraine, in a conversation that is now part of the impeachment investigation. Mr. Volker will testify in public on Tuesday.

Mr. Giuliani said that he never “conducted a shadow foreign policy, I conducted a defense of my client,” Mr. Trump. “The State Department apparatchiks are all upset that I intervened at all,” he said, adding that he was the victim of “wild accusations.”