"You can't lose every state and expect to be the nominee," Cruz told CNN's Chris Cuomo on "New Day." "Right now, Kasich's role is really being a spoiler. Kasich benefits Donald Trump."
Kasich lost 27 states before winning his home state of Ohio, Cruz said. And the governor lost both Utah and Arizona Tuesday.
Cruz argued that Kasich, who trails both Trump and Cruz in the delegate race, would need to win "more than 100% of the remaining delegates" in order reach the 1,237 required to secure the nomination. As of Wednesday, Trump leads with 741, Cruz has 461 and Kasich has 145.
"Under the rules, he won't even be on the ballot. The (Republican National Committee) rules provide that to be on the ballot you have to have won 8 states. There are only two people who meet the threshold -- Donald Trump and me," Cruz said. "Kasich cannot even be voted on at the convention."
But Cruz said he hopes to gain Kasich's support in the near future.
"I think very highly of Kasich. I would love to have his support. I think he'd be a tremendous addition to an administration," he said.
The senator had less charitable words about Trump, who threatened Cruz's wife Tuesday on Twitter after accusing Cruz of being behind a super PAC ad that attacked his wife, Melania, for posing nude as a model.
Cruz said Tuesday he is not affiliated with the super PAC and tweeted that Trump is a "coward" for attacking Heidi Cruz.
"Heidi, my wife -- she's the daughter of missionaries in Africa. She's my best friend in the world. If Donald wants to get in a character fight, he's better off sticking with me. Because Heidi is way out of his league," Cruz said Wednesday.
Cruz said Trump's attacks on his wife revealed "a lot about character."
"It reveals a lot about character. It reveals a lot about class, that Donald's instinct is to try to attack my wife and sully her. That should be beneath Donald, but the reason he's doing that is he had a very bad night," he said.
Instead of being "dragged in the gutter," Cruz said he would rather focus on solving the issues facing Americans, like the recent terror attacks in Brussels.
Cruz noted that the Brussels attack came a day after Trump advocated for reducing U.S. involvement in the North Atlantic Treaty Organization, which is headquartered in Brussels.
"Withdrawing from NATO would be a catastrophic mistake. It would hand (Russian President Vladimir) Putin a massive victory. It would hand ISIS a massive victory," Cruz said. "I think Donald Trump's foreign policy weakness, his isolationism, is frankly to the left of Barack Obama and Hillary Clinton. Neither Obama nor Hillary Clinton advocate withdrawing from NATO."
"And Trump's views would make America more dangerous," he added.