"This is not a matter of right or left, or Democrat or Republican. This is common sense. It doesn't make sense for grown adult men, strangers, to be alone in a restroom with a little girl," Cruz told CNN's Jake Tapper on "State of the Union."
"This is the height of political correctness," Cruz continued. "And frankly, the concern is not of the Caitlyn Jenners of the world, but if the law is such that any man, if he feels like it, can go in a woman's restroom and you can't ask him to leave, that opens the door for predators."
Jenner, a reality TV star and activist for transgender causes, posted
a video to Facebook on Wednesday knocking Cruz for his support of a controversial North Carolina law that requires people to use the bathroom that corresponds with their "biological sex" stated on their birth certificate, rather than how they self-identify.
After using a women's bathroom in the Trump International Hotel and Tower in New York City -- following a recent comment by Trump in which he said Jenner could use whichever bathroom she wanted at the tower -- Jenner, a Republican, quipped: "By the way, Ted, nobody got molested."
"I've spent a lot of years in law enforcement dealing with child predators that are sick individuals," Cruz told Tapper. "That doesn't mean that that is the people who are transgendered. But there are predators in the world, and just saying that you're a man, you can go in the girls' restroom if you feel like it, opens the door for criminals."
Cruz didn't spare Trump in his criticism.
"This is the height of political correctness for Donald Trump to say yes, let grown men in the bathroom with little girls," he said.
Fiorina a 'tough competitor'
In January, Carly Fiorina told CNN's Dana Bash on "State of the Union" that Cruz -- then a presidential rival -- says
"whatever he needs to say to get elected, and then he's going to do as he pleases."
Cruz told Tapper that Fiorina's words owed to her being a tough competitor.
"She was a competitor in this primary. She was a fierce competitor in a primary people take shots at each other. That's part of the process," Cruz said. "You know, we all remember when Ronald Reagan picked George Herbert Walker Bush as his vice president and they had to explain why Bush had called Reaganomics 'voodoo economics.' Listen, that happens when you come through a primary and you unite."
Cruz added: "I can tell you Carly and I have spent weeks and weeks and weeks together on the road barnstorming the state of Indiana, barnstorming the country, and I have gotten to know and respect Carly. She's an extraordinary leader."
Boehner 'let out his inner Trump'
Former House Speaker John Boehner torched Cruz in a withering interview at Stanford University last week, calling
the Texas senator "Lucifer in the Flesh" and a "miserable son of a b----."
Asked about the criticism, Cruz shrugged it off.
"I think Boehner kinda let out his inner Trump, and he had some colorful imagery there. But it's interesting, when Boehner was attacking me, he praised Hillary Clinton. He thinks she's terrific, and he praised Donald Trump. He said Donald is his friend, his golfing buddy, his texting buddy," Cruz said. "And there's a reason -- if you like, if you want to see the next president as a Boehner Republican, then Donald Trump is your man."
So why does Boehner dislike Cruz?
"If you look at Hillary Clinton and Donald Trump and John Boehner, they're all part of the same corrupt Washington system where the rich get richer (and) the powerful and the lobbyists use government power for personal benefit," Cruz said.
'Behind the Donald Trump mask is Hillary Clinton'
Cruz, who has long questioned Trump's conservative credentials, said his rival has merely been pretending to be a Republican in order to capture the nomination. He hammered the real estate magnate over his past political donations to Clinton, his vow to be "neutral"
in the Israeli-Palestinian conflict and his promise to slap a tariff on goods made in China, which Cruz said would cause a recession.
"You know who I feel the worst for? I feel the worst for Donald's supporters who believe his role," Cruz said. "But every day, if he gets closer to the nomination, he starts taking his mask off, and behind the Donald Trump mask is Hillary Clinton."
"That is quite an image," Tapper said.
"It is a terrifying image," Cruz replied.