"This is a cheap shot," Giuliani told CNN's Chris Cuomo on "Cuomo Prime Time," adding, "This is unprofessional."
Mueller's investigation of whether the President committed obstruction of justice did not conclude that Trump had committed a crime but it also "does not exonerate him," Attorney General William Barr quoted from Mueller in his summary to Congress of the special counsel's report.
"They don't have to exonerate him, you gotta prove he's guilty," Giuliani said. "Even for impeachment," he added.
After a nearly two-year investigation, Mueller did not find Trump's campaign or associates conspired with Russia, Barr said Sunday. Giuliani argued that Barr, in effect, exonerated Trump in the rest of the letter released Sunday.
Trump "is exonerated in the next two paragraphs," Giuliani argued.
"The next two paragraphs say 'not sufficient evidence' and 'no obstructive conduct,' " he said.
"That's exoneration by Rod Rosenstein, the attorney general and the Office of Legal Counsel," Giuliani said.
Mueller did not make the decision himself on whether to prosecute Trump on obstruction of justice. Barr and Deputy Attorney General Rosenstein determined the evidence was "not sufficient" to support prosecution.
Another of Trump's personal lawyers, Jay Sekulow, told Cuomo that prosecutors don't exonerate, "so I don't even know why the word is in there."
"I haven't seen it. I don't know what's in it," Sekulow said of Mueller's report, and added, "I'm sure they're working on a thorough review."
"The attorney general said he is going to disclose as much as he can consistent with the law and the regulations, and I believe he's going to do that," Sekulow said.
Trump's written answers to Mueller's questions will not be released without a court order, Sekulow said. "You don't have a right to see the President's answers," he said.
This story has been updated.