Trump slammed the Florida senator during an interview Thursday with CNN, calling the 44-year-old just a "kid." It followed a lengthy attack on Rubio that Trump delivered the previous day in South Carolina.
Later on Thursday, Rubio told a Kentucky sports radio station that Trump lashes out at his opponents when his front-runner status appears in jeopardy.
"He takes shots at everybody that gets anywhere close to him, in terms of a poll, or anytime he hits a rough spot, that's what he does," Rubio said WLAP.
"He had a really bad debate performance last week, he's not well informed on the issues, he really never talks about issues and can't have more than a 10 second sound bite on any key issue," Rubio said. "So I think he's really been exposed a little bit over the last seven days and he's a very touchy and insecure guy and so that's how he reacts. And people can see through it."
On CNN on Thursday, Trump spent significant time on disparaging Rubio.
"Marco Rubio, he's like a kid. He shouldn't be running in this race as far as I'm concerned," the 69-year-old Trump said.
Trump also downplayed Rubio's public service, claiming he doesn't do anything but sit at a desk.
"Marco Rubio sits behind a desk; sometimes and he reads stuff, he's in committees so you know that's all he does. I create jobs all day long," Trump told CNN's Alisyn Camerota on "New Day."
"Believe me, I'll know more about this than all of them put together," Trump said. "If Marco Rubio's good, how come we're doing so badly? He's a sitting U.S. senator so why doesn't he do something about it? I'm not in government, he is in government."
Trump's fire comes after Rubio knocked Trump on Tuesday, suggesting the businessman is not prepared to take the helm as commander-in-chief.
"I think that the most important thing a president will ever do is provide for the national security of our country, and I think up to now, he hasn't really answered serious questions about national security," Rubio said on Fox News. "Until he does, there should be serious concerns, not just about him but about any candidate that's not able to speak in detail, with clarity and with seriousness, about the national security threats that we face."
Trump first took aim at Rubio -- who is ascendent in polls
following a strong performance in last week's CNN debate -- during a Tuesday night tweet, then again on Wednesday
, during an appearance in South Carolina.
"I mean, Marco Rubio, as an example. He's got no money, zero. Now, I think that's OK, (but) ... I mean, he's got nothing," said Trump, speaking before the Greater Charleston Business Alliance at a joint event with the South Carolina African-American Chamber of Commerce in North Charleston.
Trump -- who is often mocked for his own signature coif -- even went after Rubio's hair.
"(Rubio) announced he was going to run because he's overly ambitious, too young -- and I have better hair than he does, right?" Trump said to cheers from the crowd.
But Trump told CNN on Thursday when it comes to foreign policy, he prefers to be "unpredictable" over revealing how he would address top national security issues like the threat of ISIS and U.S. military interventions in Iraq and Syria. He also slammed President Barack Obama for giving the U.S.'s enemies too much insight into U.S. policies.
"I don't want the other side to know what my views are, where I'm coming from," Trump said. "You've got to be cool and you've got to be unpredictable."
Trump also mocked Obama for publicizing ISIS successes.
"Every time they kill mid-level accounting person from ISIS they have a news conference," he said.