GOP presidential candidate Marco RubioMarco Antonio RubioOvernight Defense: Tillerson, Trump deny report of rift | Tillerson says he never considered resigning | Trump expresses 'total confidence' in secretary | Rubio asks Army to kick out West Point grad Rubio asks Army to kick out West Point grad with pro-communist posts GOP establishment doubts Bannon’s primary powers MORE (R-Fla.) on Tuesday continued to push back against front-runner Donald TrumpDonald John TrumpIvanka Trump pens op-ed on kindergartners learning tech Bharara, Yates tamp down expectations Mueller will bring criminal charges Overnight Cybersecurity: Equifax security employee left after breach | Lawmakers float bill to reform warrantless surveillance | Intel leaders keeping collusion probe open MORE's campaign slogan, "Make America Great Again,” instead of going after the billionaire businessman himself.

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“There’s one other candidate running, he says he’s going to make America great again,” Rubio told about 200 people gathered in a community center in Nevada, according to The New York Times.

“I understand what he means by that. I don’t mean that as a slight," the Florida senator insisted, according to the newspaper.

“I would remind everyone America is great,” Rubio continued. “There’s no nation on earth I would trade places with. There’s no other country I would rather be. The issue is not that we’re not great. The issue is whether we will remain great. The issue is, we can be even greater than we are now. We can be even more prosperous, more powerful."

Rubio, who has shied away from directly attacking Trump, has repeatedly taken issue with the slogan that has become synonymous with the real estate mogul’s 2016 White House bid.

"In comparison to where the world is today, yeah, America's still a great country. But that's not due to our policies, that's despite our policies," Rubio told CNBC as part of an interview released last week.

Before that, Rubio said on Fox News that "America is a great country. ... We could be even greater."

Rubio, who has cast his own campaign as a bid for "A New American Century," has remained in the top tier of GOP candidates, placing fifth of 17 in the latest Public Policy Polling survey released on Tuesday.