Donald Trump is an "alpha male" in the battle against Sen. Ted Cruz, Rush Limbaugh said on Friday, adding that he was not sure how to describe Cruz.

The conservative radio host was referring to remarks Trump delivered earlier in the day in which he addressed Cruz's grievance against him, which is that Trump had "attacked" his wife and father during the Republican primary campaign.

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Trump pointed out that a group associated with Cruz had also attacked Trump's wife, and he argued that a statement about Cruz's father was valid. "All I did was point out the fact that on the cover of the National Enquirer, there was a picture of him and crazy Lee Harvey Oswald having breakfast. Ted never denied that it was his father. Instead he said ... I had nothing to do with it."

"You know what just happened here? This is alpha male versus I don't know what," Limbaugh said on his radio program. "The only reason Trump went here" again, Limbaugh said, was "because Cruz went to the Texas delegation and let it be known that his pique ... is over the way Trump talked about his wife and his father.

"So what did Trump do? [He] triples down, finds out where you're vulnerable and comes right back at you with a sharp knife. This is [an] alpha male," Limbaugh added.

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Cruz on Wednesday refused to endorse Trump while speaking at the Republican National Convention. He left the stage to a chorus of boos from delegates at the event, and he has been widely panned for the move by party officials and conservative commentators.

Speaking in Cleveland on Friday, Trump insisted Cruz had done more to attack his wife than the reverse.

"I didn't start anything with the wife. A PAC, which he is very friendly with, released a cover story on my wife, who is a tremendously successful and elegant model. She was on the cover of GQ magazine ... an artsy picture, but she was a model. Really successful. She didn't need to marry me. She was making a lot of money ... I had to work hard to get her to marry me," Trump said. "So they release this picture."

On the issue of an endorsement from Cruz, Trump said he was no longer interested. "You know he'll come and endorse over the next little while ... because he has no choice. But I don't want his endorsement. What difference does it make?"

"Ted, just stay home, relax, enjoy yourself," Trump added.