The Kentucky Republican is languishing in the low single digits in the polls as Trump and Cruz lead the pack in the GOP primary, but Paul said the prospect of a Trump presidency concerns him.
"I do worry a little bit more about Donald Trump," Paul told CNN's Wolf Blitzer on Thursday. "The main reason I do is that I believe he wants more power to come to him and 'he'll take care of us all' if we just give him more power, but I'm from a limited government tradition."
The attack was an echo of attacks Paul made Wednesday, including comparing Trump to Gollum, a villain from "Lord of the Rings" who is corrupted by his quest for the powerful ring.
"I think what Trump wants is bad for America," Paul said.
But Paul said he has concerns about both the billionaire businessman and Cruz, attacking both of them on foreign policy.
"I don't think (Trump) has a consistent foreign policy," Paul said, but "I do think that he and Ted Cruz that want to make the 'sand glow' ... I think if you do indiscriminate bombing in the Middle East, you may well create more terrorists than you kill."
He also attacked Cruz for flip-flopping on issues based on what's politically expedient.
"I think Ted Cruz's problem is one of authenticity right now," Paul said.
He mentioned that the Texas senator voted with Paul on a bill to rein in government surveillance, but that Cruz said in a debate that he voted for the bill because it allows the government to collect more records of terrorists.
Paul said the libertarian-minded voters that support him are turned off by that.
"Our people pause at that and say, 'My goodness, is he trying to have it both ways?'" Paul said. "That kind of leap back and forth and trying to have it both ways really we think is Cruz's biggest problem right now."