Giuliani also said Monday that "the odds are against" a Trump interview with Mueller, but that he "wouldn't be shocked" if the President went through with it because he "wants to do it so badly".
He also claimed on Thursday that Russia was "very unhappy" he had won the election, although at his joint news conference with Putin, the Russian leader said he had wanted Trump to win.
Cohen is willing to tell Mueller that Trump lied about his knowledge of the infamous Trump Tower meeting in 2016 between senior members of his campaign and a Kremlin-linked Russian lawyer touting dirt on Hillary Clinton. "At some point I will have no choice but to use the powers granted to the Presidency and get involved!" he tweeted then.
A Justice Department spokeswoman declined to comment about Trump's call for Sessions to end the investigation.
Sen. Susan Collins, R-Maine, said it "was entirely inappropriate and intemperate" for Trump to make such a request of Sessions.
Trump escalated his attacks against the Mueller-led probe early Wednesday, urging Attorney General Jeff Sessions to shut down the wide-ranging inquiry. "When I was a prosecutor, obstruction of justice was often hard to prove, requiring difficult-to-obtain evidence that the individual's actions were truly meant to interfere with an ongoing criminal investigation".
Trump's tweet had raised the concern that he may try to more directly bring Mueller's probe to a premature end.
Polar bear killed after attacking man on island off northern Norway
In 2015, Czech Jakub Moravec was pulled out of the tent by a polar bear, but escaped with slight damage. Reportedly two guards went ashore in advance of passengers in order to sweep the area for polar bears.
Jens David Ohlin, a law professor at Cornell University, said the tweets would likely not be seen as an order to Sessions, but as "Trump venting his continued frustration with the fact that he can't control the Russian Federation investigation".
His lawyer Rudy Giuliani added: "He used a medium he uses for opinions, Twitter".
Some Democratic politicians said Mr Trump's tweets showed an intent to obstruct justice. Prosecutors told a jury Manafort hid much of the $60 million he earned from lobbying as an unregistered foreign agent on behalf of pro-Russia Ukrainian officials by stashing it in undisclosed overseas accounts. No longer do we need to debate whether interfering with an FBI investigation can be obstruction; we now have the president of the United States trying to shut down the trial (one of two) of his former campaign chairman.
"Looking back on history, who was treated worse, Alfonse Capone, legendary mob boss, killer and "Public Enemy Number One", or Paul Manafort, political operative & Reagan/Dole darling, now serving solitary confinement - although convicted of nothing", Trump tweeted.
Speaking to Democracy Now on July 30, MIT emeritus professor Noam Chomsky referred to the media's obsession with Russian collusion as "marginalia".
"I just think they ought to let the Mueller investigation continue on its own course", said Senator John Thune, adding: "I hope it's done soon".
Manafort served as Trump's campaign chief from May to August 2016 and the president asked Wednesday: "why didn't government tell me that he was under investigation".
"I would describe it as a tiny bit of movement, not anything dramatic, but at least it is worth responding to", Giuliani said of the offer in an interview with Bloomberg News.