He went on to call the presidential race "a reality show that's beyond belief".
"I mean, it buries the Kardashians," he said. "We're electing a new leader. Is this the best we have? It's really scary. I keep wondering what people internationally think as they watch these debates [with] Trump and (Ted) Cruz. It's embarrassing."
He singled Cruz, another Republican candidate, out for particular criticism over his re-enactment of movie scenes - including Crystal's character from The Princess Bride, Miracle Max.
"What a maniac," he said. "First time I saw [that] I thought, 'what is he doing?' He did this imitation of me that's sort of a version of me but not me. And he kept doing it.
"The whole thing was weird. He's weird. He's a strange one."
Crystal's tour is billed as An Evening of Sit Down with Billy Crystal hosted by Andrew Denton. Denton, a veteran Australian television presenter and interviewer, will be prompting Crystal for stories about his life and career.
The show follows Crystal's Tony Award-winning 700 Sundays, an autobiographical one-man show, which toured Australia but not New Zealand.
"I'm absolutely delighted to bring my new show to New Zealand. I have visited this beautiful country before but I am particularly excited to perform there for the very first time," Crystal said in a statement.
"The show will be spontaneous, funny and unpredictable. I tell stories, I perform, we show film clips. And yes, I will stand up. It's not only a conversation with Andrew, it's with the audience as well."
- nzherald.co.nz