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By Rebecca Dube

President Obama opened up to TODAY's Jenna Bush Hager about fatherhood and raising teen girls in the public eye, in an exclusive interview to air on TODAY on June 12.

"The time goes by so quick," Obama said, noting that his advice to new dads is to savor every moment. "Understand that there's nothing that's going to be more precious in your life... And when you're on your death bed, that's the stuff you're going to remember — you holding hands with your daughter."

WATCH: Obama on the challenges of raising a family in the White House

Obama has two daughters: Malia, 15, and Sasha, who turned 13 this week. Bush Hager, the daughter of President George W. Bush, has a rare perspective on the experience of growing up in the White House.

Which is harder, Bush Hager asked Obama, being president of the United States or being the protective father of teen daughters?

"I think my dad would maybe have a comment on this," she quipped.

Obama said he jokes that "the main reason I ran for re-election was to sustain that [Secret Service detail] all the way through their high school years." But in truth, he said, "I don't worry too much about their social lives."

Clearly on his mind is the fact that his girls, like all children, are growing up fast. "The main thing I'm going through right now is just the time goes by so quick. And you know, Malia will be gone [to college] in two years. You know, Sasha'll be gone in five and it seems like yesterday," Obama said.

When he talks to new dads, Obama says he tells them, "Don't just spend time with your kids because it's good for the kids; understand that there's nothing that's going to be more precious in your life."

Obama also discussed his initiative My Brother's Keeper, which provides support for young minority men.