Speaking at a White House-sponsored forum on women's issues Tuesday, Obama hailed Clinton as the first female presumptive nominee of a major U.S. political party, proclaiming she had "raised the expectations of our sons and daughters of what is possible."
And he declared himself an unabashed promoter of women's rights.
"I may be a little grayer than I was eight years ago, but this is what a feminist looks like," he said.
Citing his own children, Obama said the country's younger generation rarely feels hampered by their gender, even as inequalities such as a wage gap persist.
"They think it's weird we haven't already had a woman president," Obama said. "They expect the world to catch up to them. And I have no doubt that we will."
Obama, who endorsed Clinton last week, hadn't previously spoken publicly about his former secretary of state's rise to the top of the Democratic Party. He was supposed to campaign with her Wednesday in Wisconsin, but the trip was canceled after Sunday's terrorist shooting in Orlando.
In his remarks at the summit, Obama peppered his address with allusions to Clinton, at one point calling for more women in corner suites -- noting the Oval Office itself would qualify.
But he said that until a new president is elected, he would continue working toward pro-women policies.
"They keep waiting for this whole lame duck thing to happen. Let me tell you, it will happen as soon as I have elected a really good successor to carry on our policies," he said. "Until then, we're working pretty hard."
Societal barriers to women's success -- often subtle or unspoken -- persist, Obama said. He challenged a culture that he said "punishes women for their sexuality but gives men a pat of the back for theirs."
Fathers, he said, shouldn't be congratulated simply for "changing a diaper." And a hostile Internet environment "where women are routinely harassed and threatened when they go online" needs to change, he said.
Even his wife, first lady Michelle Obama, has "had times where she's had doubts, where she's had to worry whether she was acting the right way, or looking the right way, or too assertive, or too angry," the President said.
Those feelings, he said, were shifting with a new generation.
"They believe every door is open to them," he said of his daughters. "They're not engaging in any kind of self-censorship. They're not going to hold themselves back. It wouldn't occur to them they couldn't rise to the top of whatever field they choose."
He tied those changes in attitude to the broader movement to secure equal rights for women, placing Clinton and the first lady in a line of predecessors that included Susan B. Anthony and Lucretia Mott. He also hailed the work of civil rights heroes like Harriet Tubman, who the administration says will eventually appear on the $20 bill.
"Our country is not just about the Benjamins," Obama said. "It's about the Tubmans, too."