"They're a joke," Giuliani told Fox News. "Over my dead body, but, you know, I could be dead."
The Special Counsel, who is investigating possible ties between the Trump campaign and Russia, has continued to request an interview with the President.
Last month, the White House sent written answers in response to the Special Counsel's questions about possible collusion. The White House has resisted answering questions on possible obstruction of justice.
Giuliani sarcastically said that the only thing left to ask the President was about "several unpaid parking tickets that night, back in 1986, '87 that haven't been explained".
If the President officially refuses an interview request, the Special Counsel's team could theoretically seek to subpoena him to compel his testimony. Such a move would almost certainly trigger an immediate court fight.
The Supreme Court has never directly ruled on whether a president can be subpoenaed for testimony in a criminal investigation, though the justices have said that a president can be forced to turn over records that have been subpoenaed and can be forced to answer questions as part of a lawsuit.
The Special Counsel's investigation has spun out charges and strong-armed guilty pleas from Trump underlings while keeping in suspense whether the President — "Individual-1," in Mueller's coded legalese — will end up accused of criminal behaviour himself.
This past week, his legal exposure grew as his former personal lawyer, Michael Cohen, was sentenced to three years in prison after admitting he issued hush-money payments to women who alleged sexual trysts with Trump. Prosecutors and Cohen say he acted at the President's direction, which Trump and Giuliani deny.
Trump and Giuliani have repeatedly tried to paint Cohen as untrustworthy, with the former New York City Mayor calling him a "pathological liar".
Trump and Giuliani have also accused prosecutors of intimidating the President's associates into making false claims.
"Remember, Michael Cohen only became a 'Rat' after the FBI did something which was absolutely unthinkable & unheard of until the Witch Hunt was illegally started," Trump tweeted. "They BROKE INTO AN ATTORNEY'S OFFICE!"
It was not a break-in. The FBI executed a search warrant obtained from a judge in conducting a raid in April on Cohen's home, office and hotel room and seizing records on a variety of matters, among them a US$130,000 payment made to porn actress Stormy Daniels by Cohen. The application for the warrant was approved high in the Justice Department.
In response to Trump's tweet, former FBI Director James Comey tweeted, "This is from the President of our country, lying about the lawful execution of a search warrant issued by a federal judge. Shame on Republicans who don't speak up at this moment — for the FBI, the rule of law, and the truth".
Trump compared his situation to one involving former President Barack Obama's 2008 campaign. The Federal Election Commission docked the Obama campaign US$375,000 for regulatory civil violations. The fines stemmed from the campaign's failure to report a batch of contributions, totaling nearly US$1.9 million, on time in the final days of the campaign.
But legal analysts said the accusations against Trump could amount to a crime because they revolve around an alleged conspiracy to conceal payments from campaign contribution reports — and from voters. It's unclear what federal prosecutors in New York will decide to do if they conclude that there is evidence that Trump himself committed a crime.
Trump has not yet laid out a detailed defence, though he could conceivably argue that the payments were made not for the purposes of advancing his campaign but rather to prevent salacious stories from emerging that would be personally humiliating to him and harm his marriage.
That argument was advanced by former Senator John Edwards, a North Carolina Democrat, in a similar campaign finance case that went to trial in 2012.
But that may be tougher for Trump than it was for Edwards given the proximity of the President's payment to the election — timing that, on its face, suggests a link between the money and his political ambitions.
Edwards was acquitted on one count of accepting illegal campaign contributions, but jurors couldn't reach a verdict on the five remaining counts, including conspiracy and making false statements.
- AP
