Giuliani, who said talks between the two sides were continuing, saw Mueller's stance as a hardening in the position prosecutors are taking after offering to allow Trump to answer questions in writing.
"When the government comes knocking on your door to ask you questions, it's not to help you, it's to help the government", the judge told "Fox & Friends".
Mueller's team and Trump's lawyers have been haggling over a potential interview with the president for months.
Rudy Giuliani said Wednesday that President TrumpDonald John TrumpNorth Korea to cooperate with US in nuclear talks: report Nike to air Kaepernick ad during 'Thursday Night Football: report Brothel owner who won Nevada GOP primary being investigated over sexual assault allegations MORE's legal team has responded to special counsel Robert MuellerRobert Swan MuellerSasse: US should applaud choice of Mueller to lead Russian Federation probe MORE's latest proposal for an interview with the president, and expressed optimism the two sides could come to an agreement.
Mueller is also investigating whether Trump may have tried to obstruct the Russian Federation investigation after winning office, but Giuliani said on Thursday that no questions on the obstruction issue would be part of the first round of questions.
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For now, British Airways states that its website is "working normally so future bookings will not be affected", per its post. The NCA is set up to tackle the most serious and organised crime posing the highest risk to public security in Britain.
"It would be in written form and if you want to follow up on our answers, justify it", Giuliani said. "The president will say "looks fine to me" and sign it".
Trump's legal team has argued that the president has the power to hire and fire appointees and the special counsel does not have the authority to ask him to explain those decisions. "He can't, and he shouldn't even try to do so".
"They want a commitment" to a follow-up interview, Giuliani said.
Trump and Giuliani have led an onslaught of attacks on Mueller's credibility, claiming that the special counsel was biased and that the entire probe was a 'witch hunt'. "We've said no, and let's see how they deal with it".
Giuliani has also demanded that the probe suspend its activities with the midterm elections approaching, but the former mayor said Thursday he was not certain of Mueller's intentions.