Story highlights Key supporters of Marco Rubio floated the prospect of the Florida senator joining Donald Trump's ticket

On Monday, Rubio put out a statement saying he would not seek and does not want to be considered for the position

(CNN) Marco Rubio on Tuesday declined to offer Donald Trump a formal endorsement and said he's not interested in being Trump's vice president, although will support the GOP nominee in accordance with a pledge he made during the primary fight.

"I stand by the things that I said" during the campaign, the Florida senator told CNN's Jake Tapper on "The Lead," referring to his past criticisms of the presumptive nominee, including calling him a "con man" and saying he shouldn't be given access to nuclear codes. "But I'm not going to sit here right now and become his chief critic over the next six months, because he deserves the opportunity to go forward and make his argument and try to win."

But Rubio stopped short of offering Trump his clear backing.

"I signed a pledge, put my name on it, and said I would support the Republican nominee and that's what I intend to do," he said.

Rubio's comments come as Trump's sudden status as the party's presumptive presidential nominee have the campaign transitioning from a fierce primary battle to preparing for the general election, unifying support from Republican leaders and beginning the process of selecting a running mate.

Rubio: Trump would be better served by VP who embraces the things he stands for. "That's certainly not me." https://t.co/3G2frjJvzN — Zach Wolf (@zbyronwolf) May 10, 2016

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