Giuliani alluded to the deep worry, bordering on panic, that had taken hold of the White House over the Daniels affair.
Giuliani echoed that suggestion on Fox News, telling Hannity that Comey should be prosecuted.
Cohen is under investigation by federal prosecutors for his role in the payment as well as other murky business deals.
Rudy: Yes, Trump paid Cohen back the $130k.
She is seeking to be released from the $130,000 non-disclosure agreement she signed shortly before the 2016 presidential election to stay quiet about the alleged affair, with Mr Cohen having admitted to paying for it. Trump has separate lawyers representing him in the Daniels litigation.
Giuliani told Hannity that although "everybody was nervous about this from the very beginning", he wasn't anxious.
"I love Rudy, but they better have an explanation for that", Ingraham said.
"It's not campaign money".
The money was "funneled through a law firm and then the president repaid it", Giuliani added.
"Michael saw an opportunity to settle it for not very much money, and he took it", Giuliani said.
Asked if Trump knew about the arrangement, Giuliani said: "He didn't know about the specifics of it, as far as I know".
Daniels claims she had sex with Mr. Trump in 2006, months after his third wife gave birth to his youngest child. Daniels alleges that she had a relationship with Trump more than a decade ago - which Trump denies and which Daniels' was not to speak about under the terms of the settlement agreement.
Daniels' attorney Michael Avenatti called Giuliani's statement "a stunning revelation".
Democrats, and Stormy Daniels attorney Michael Avenatti, insisted that Trump had committed a felony. That has stirred accusations that Cohen's payment to the porn actress amounted to an illegal campaign contribution. Hannity has described his personal dealings with Cohen as centred on real estate advice and said that it "never rose to any level that I needed to tell anyone that I was asking him questions".
"No", said the president, who also claimed that he didn't know where Cohen obtained the money to pay Stormy Daniels.
Cohen has said he made the payment independently, without Trump's knowledge and without looping in the Trump Organization - a move that would be unusual and unethical, as lawyers don't generally make payments on behalf of clients without their knowledge.