Once considered as a future of the Republican party, Rubio, 44, withdrew himself from the White House race after he lost his home state of Florida to Trump, 69 in primary.
"I've never had those conversations with anyone in his campaign, so I'm not saying that anyone has offered it to me or even suggested it for me. I'm just saying to you that I believe he would be best served by someone who more fully embraces the things he stands for, and that is certainly not me," Rubio told the CNN in an interview when asked if he is in consideration for vice presidential running mate of Trump.
In his first national interview after he quit the presidential race, Rubio said he would not support the Democratic presidential front-runner Hillary Clinton, 68, in the November general elections.
"I signed a pledge that said I would support the Republican nominee and I intend to continue to do that," he said, indicating that he is pledge-bound to support Trump in the elections.
"On the one hand, I don't want Hillary Clinton to be the president of the US. I don't want her to win this election. On the other hand, I have well-defined differences with the presumptive nominee of the Republican Party.
"Like millions of Republicans, you try to reconcile those two things. I intend to live up to the pledge that we made. But, that said, these concerns that I have about policy, they remain and they're there. That doesn't mean that Donald needs to change his positions in order to get my support or what have you. He should be true to what he believes in and continue to campaign on those things and make his case to the American people," Rubio said.
The top Republican Senator said he would not use the next six months to be critical of Trump as he advances his presidential campaign.
"Here's what I'm not doing to do over the next six months is sit there and just be taking shots at him. He obviously wasn't my first shot the because I was running for president. He has won the nomination. Now he deserves the opportunity to go out and make his case to the American people. And that's what he's going to do. I don't view my role over the next six months to just sit here and level charges against him," he said.
"I know what I said during the campaign. I enunciated those things repeatedly. And voters chose a different direction. I stand by the things that I said. But I'm not going to sit here 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," Rubio added.
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