"Frightening a few people is not so bad if you can please a multitude of people," said the pair in a statement.
Local resident Jonathan Wood said he saw children screaming in nearby woods as they ran away from a clown that looked like the Stephen King character.
Both P&O Cruises and local police dismissed earlier suggestions that the fight broke out after a passenger dressed as a clown gatecrashed a formal reception.
Former Vice President Joe Biden demanded a higher level of discourse in the 2020 campaign, claiming he has "so many nicknames" to give President Donald Trump, but settling for now on "clown."
"I enjoy being a lawyer more than I do being a politician," Giuliani said. "This is what I think I do best."
Avenatti said an election between him and Trump in 2020 would be "extremely contentious" and "very close."
"They joke that the president and Congress are all clowns. Well, in my professional opinion, they are the worst clowns I've ever seen."