"I've never had any substantive conversation with Boehner in any respect," the GOP presidential hopeful said at a news conference in Indiana.
"So when he says I'm the worst guy he's ever worked with, he's never worked with me. John Boehner's remarks reveal everything that's wrong and corrupt about Washington, everything you're angry with. When John Boehner calls me Lucifer, he's not directing that at me. He's directing it at you."
Cruz's comments came a day after Boehner shared some choice words about the presidential candidates during an appearance at Stanford University.
When asked about the Texas senator, fellow Republican Boehner said: "Lucifer in the flesh," according to The Stanford Daily. "I have Democrat friends and Republican friends. I get along with almost everyone, but I have never worked with a more miserable son of a bitch in my life."
Boehner also impersonated Democratic front-runner Hillary Clinton, saying, "Oh I'm a woman, vote for me." Boehner called Democratic challenger Bernie Sanders a nice guy and said this about John Kasich: The Republican governor of Boehner's home state "requires more effort on my behalf than all my other friends … but he's still my friend, and I love him."
Boehner, who retired from Congress last fall, didn't leave himself out of the name calling: "You can call me boner, beaner, jackass, happy to answer to almost anything," he said, according to the Daily. He said would vote for "texting buddy" Donald Trump if Trump wins the GOP nomination.
Boehner's speaking agency and the Clinton and Kasich campaigns did not immediately reply to CNBC's request for comment.