GOP presidential candidate Marco RubioMarco Antonio RubioNikki Haley: New York Times ‘knew the facts’ about curtains and still released story March For Our Lives founder leaves group, says he regrets trying to 'embarrass' Rubio Rubio unloads on Turkish chef for 'feasting' Venezuela's Maduro: 'I got pissed' MORE (R-Fla.) on Tuesday continued to push back against front-runner Donald TrumpDonald John TrumpHannity urges Trump not to fire 'anybody' after Rosenstein report Ben Carson appears to tie allegation against Kavanaugh to socialist plot Five takeaways from Cruz, O'Rourke's fiery first debate 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.