(CNN) -

Sen. Rand Paul hopes to infuse the Republican Party with some of his libertarian views, but the Kentucky Republican said Friday he'd still support the GOP presidential nominee in 2016 even if he didn't entirely agree with that person.

"I think a libertarian twist or a libertarian influence in the Republican Party is good, but I've pretty much just stayed with the party and plan on doing so," he said at Harvard's Institute of Politics.

Paul, who's considering a White House bid, had been asked by a student whether he would support a libertarian candidate in the next presidential election if Paul doesn't become the nominee.

The first-term senator described himself as "libertarian-ish," but said he's never endorsed libertarian candidates.

He was corrected by the student, who pointed out that Paul supported his father, ex-Rep. Ron Paul, when he ran for president as a libertarian in 1988.

"You're right. I did. I stand corrected," Paul said, laughing.

"I did, and I hope I don't have to oppose him in anything," he joked. "Somebody asked me the other day 'What if your dad runs?' And I was like 'I'm not going there, alright?'"

Making the GOP slightly more libertarian is just part of Paul's recent mission to broaden the Republican Party. The senator reiterated his message that it also needs to look different in terms of race and age.

"You go to a Republican event and it's all white people -- not because we're excluding anybody, but because we just haven't done a good enough job encouraging people to come into our party," he said at the event, which was hosted by his 2010 GOP primary rival, Trey Grayson. He's now the institute's director.

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Senator says GOP needs to be bigger