The relationship between Florida Sen. Marco Rubio and former Florida Gov. Jeb Bush, who once served as his mentor, is increasingly coming apart, as both men seek to make their marks in the crowded field of 2016 GOP White House contenders.

Last week, Bush attacked Rubio by name for the first time, comparing his fellow Floridian to President Barack Obama, who -- like Rubio -- was a one-term senator when he first ran for the presidency in 2008, the Los Angeles Times reported.

"Look, we had a president who came in and said the same kind of thing -- "new and improved," "hope and change" -- and he didn't have the leadership skills to fix things," Bush said on CNN.

Rubio, in turn, seemed to seize on fears of a "Bush dynasty" and characterized the brother of former President George W. Bush and son of former President George H.W. Bush as a classic "establishment candidate," MSNBC noted.

"If we keep electing the same kind of people with the same ideas, the next person in line, the person all the experts tell us we have to vote for -- if we keep doing that, nothing is going to change," Rubio said at an event in Dubuque, Iowa on Friday.

Nevertheless, Rubio later insisted that he still had "tremendous admiration and respect and affection" for Bush, 62, the Los Angeles Times reported. "But I'm running for president," the 44-year-old explained. "I'm not running against him or anybody else. So I'm going to continue to focus on what I think our country needs to do."

Rubio has steadily improved in the polls since the last Republican debate, and the Bush camp is increasingly seeing him as a threat to the former governor's own presidential ambitions, MSNBC commented.

The son of Cuban immigrants jumped from seventh place to fourth place in a recent CNN national poll, and trails only Donald Trump and Carly Fiorina in the key early-primary state of New Hampshire, the Boston Globe pointed out.

Donna Sytek, a New Hampshire GOP heavyweight and former speaker of the state's House, told the newspaper that Rubio was benefiting from a "honeymoon period" in the Granite State.

"Gee, fresh face. Speaks well. Has interesting ideas. Doesn't have all the baggage that the past front-runners have. Let's give him a look," local Republicans say about him according to Sytek. "He's clearly younger than the rest of the pack. ... But wouldn't that be a contrast with Bernie Sanders? Or Hillary Clinton? Or Joe Biden?"