Ted Cruz said on Tuesday that Donald Trump "embodies New York values," and that Trump's constant attacks on him are a sign that the businessman is worried about his front-runner status in the race.

Cruz made the comment on the Howie Carr Show, after the host asked him about Trump playing Bruce Springsteen's "Born in the USA", a reference to the allegation, recently trumpeted by Trump, that Cruz may be ineligible to serve as president because he was born in Canada.

"Well, look, I think he may shift in his new rallies to play 'New York, New York' because Donald comes from New York and he embodies New York values," Cruz said, referring to the famous Frank Sinatra song.

The Texas senator went on to say that Trump seemed "rattled" by his rising stature in the race. He added that Trump had been "unloading at every stop with direct attacks." Cruz said he did not "intend to respond or reciprocate."

On Tuesday, however, Cruz twice appeared to take jabs at Trump, telling reporters earlier in the day that supporters of Democratic candidate Hillary Clinton were "eager to support Donald Trump and the attacks that are being tossed my direction."

In the radio interview, Cruz reiterated this argument. In response to a clip of Clinton saying Trump was "a Democrat before he was a Republican," Cruz said, "Well, I would say, Hillary would know well how to identify Democrats. She has been a partisan Democrat herself obviously and, uh, she and Donald know each other well and I do think it's interesting that Hillary Clinton's key supporters are doing everything they can to echo Donald's attacks on me."

Democratic attacks on him, he added, "may be driven by the fact that the polling right now shows Donald loses to Hillary and loses by a pretty big margin but I beat Hillary and I think that's got the Hillary folks a little bit concerned and so they're doing everything they can to amplify Donald's attacks."

Cruz also addressed Trump's comment that "not a lot of evangelicals come out of Cuba" by inviting the reality TV star to go to church with him.

"Any time someone is attacking your faith that starts to suggest they're getting really nervous about what's happening in the race," Cruz said. "I would be happy to invite Donald to come with me to church any time he would like. He would certainly be welcome there. And, uh, you know, at the end of the day, my focus is not to engage in the mudslinging."