Giuliani noted that Trump's lawyers will not sit for an interview with Special Counsel Robert Mueller unless they get all relevant documents about Russia's alleged role in the USA presidential election in 2016.
Giuliani agreed with the letter's finding that Trump has unlimited power to pardon while saying, in a separate appearance on NBC's "Meet the Press", that pardoning himself would probably lead to impeachment.
"It would be an open question", he added.
"I think the political ramifications would be tough", Giuliani told ABC's This Week.
Mueller is also looking into whether Trump unlawfully sought to obstruct the Russian Federation investigation.
Jonathan Turley, a law professor at George Washington University, said he believed the president has the authority to pardon himself, and using pardons as a piece of an obstruction case might be problematic "because the nature of the act is to bar prosecutions or set aside convictions".
Mueller's investigation has so far resulted in the guilty pleas of five people, including three former Trump campaign staffers, and the indictment of 14 other people and three companies.
"Do you think he has the power to pardon himself?". This fact is coupled with a legal protection that makes the president not readily available to be interviewed unless the information can not be obtained by any other means. I know based on presidential rulings, meaning the discretion of the president, Justice Department is given a certain amount of independence.
The letter is "pretty extraordinary" in that it states an action that would otherwise be illegal isn't illegal when a president does it, former Manhattan federal prosecutor Mimi Rocah said.
Giuliani said Trump's lawyers would tell Mueller's team that "you've got everything you need, 1.4 million documents, 28 witnesses" to conclude its investigation.
In a column on Sunday morning, Vox's Matthew Yglesias characterized the memo from Trump's legal team as "a recipe for tyranny" and a "clear and present danger to the rule of law".
A special counsel is investigating Russia's role in the 2016 election, and whether Mr Trump obstructed justice. "Other presidents have pardoned people in circumstances like this both in their administration and sometimes the next president, even of a different party will come along and pardon", he said.
Mueller's office declined to comment, while the White House and the two attorneys who wrote the letter - Sekulow and Dowd - did not reply to requests for comment. Previously, the Trump team had denied, unconvincingly, that the president had anything to do with that missive. The attorneys then present the relevant interview transcript in its entirety to show that Trump knew that the Russian Federation investigation would likely be protracted if he fired Comey, but that he had "to do the right thing for the American people".