Davidson and Cohen exchanged a series of messages in January to have Clifford appear on Sean Hannity's Fox News show and have her refute a 2011 interview In Touch Weekly published that month, describing her encounter with Trump, according to a complaint filed Wednesday in state court in Santa Monica, California.
Avenatti's remark calling Giuliani a pig was in response to the former NY mayor's comments about Avenatti's client: adult film star Stormy Daniels.
The former New York City mayor who joined President Trump's legal team in April, claimed at the "Globes" Capital Market Conference in Israel on Wednesday that the first lady "believes her husband and she doesn't think it's true", regarding the affair.More news: GOP's Cox faces tough slog in race for California governor
"I respect women - attractive women and women with value - but a woman who sells her body for sexual exploitation, I don't respect", Giuliani said, The Hill reported.
Following Giuliani's initial remarks, where he demeaned Daniels' looks and said she "has no reputation" given her line of work, he was swiftly rebuked by her attorney Michael Avenatti.
"Thursday afternoon, the first lady's communications director fired back at Giuliani".
This week, Daniels filed another lawsuit alleging that her former lawyer Keith Davidson and Cohen worked together "in an attempt to use and manipulate Ms. Clifford in a manner created to benefit Mr. Cohen and Mr. Trump". "There was a significant cover-up here as part of an attempt to deceive the American people and Mrs. Trump and we intend on getting to the bottom of it".More news: NTSB releases preliminary report on fatal Model X crash
Giuliani's comments may be part of a wider political strategy to discredit Daniels' lawsuit against Trump, but they're extremely unsafe for a population of women already fighting to be respected.
GETTYMelania Trump: Does First Lady "believe" Donald over Stormy Daniels affair rumours? Trump now admits he reimbursed his lawyer, Michael Cohen, for the payment.
However, Melania's spokeswoman is denying Rudy's claims and even went as far as saying that a conversation over the matter never happened. Davidson said in his lawsuit that he only ever sought to help Daniels.
On Thursday, Giuliani was asked to explain his comments.More news: Hitman 2 Officially Announced; Will Be A Direct Sequel To Hitman
"Sorry, I don't respect a porn star the way I respect a career woman or a woman of substance", he said.