He takes pride in having banned bosses from paying men higher salaries as his first act as president, while his Democrat party accuses the Republicans of mounting a "war on women".
Yet Barack Obama was accused of sexism himself, after remarking publicly on the good looks of California's female attorney general.
Mr Obama was paying tribute to Kamala Harris, who is 48 and unmarried at a fundraising event in San Francisco.
"She's brilliant and she's dedicated; she's tough," he told his audience. "She also happens to be, by far, the best-looking attorney general."
Amid laughter from the crowd, the president added: "It's true! Come on!" A reporter assigned to follow Mr Obama for the day said he noted "a couple of times that she is, objectively, easy on the eyes".
The remark prompted accusations of disrespect and hypocrisy. "Not awkward and perfectly fine for him to say, right?" the Republican National Committee wrote sarcastically on Twitter.
Sarah Elizabeth Cupp, a conservative author and broadcaster, described Mr Obama's comment as "unsettling". Irin Carmon, a prominent liberal commentator, wrote on the Salon news website that the president "should know better", noting that it was "hardly the first time Obama has been smarmily sexist".
Obama later apologised "for the distraction created", his spokesman said. The president called Harris after his comments generated criticism on social media and from political opponents, White House press secretary Jay Carney said.
"They are old friends and good friends, and he did not want in any way to diminish the attorney general's professional accomplishments and her capabilities," Carney said.
Mr Obama was reported in February to have told Nicole Malliotakis, a 32-year-old Republican member of the New York state assembly, that she "didn't look a day over 23".
Amid jokes from bystanders that Ms Malliotakis should defect to the Democrats, Mr Obama reportedly said: "Come on, honey! I said you're pretty! I said you look 23!"
In 2008, when he was campaigning for the presidency, Mr Obama apologised after calling a female television reporter "sweetie", admitting it was a "bad habit". Mr Obama owes his re-election partly to the support of women, having beaten Mitt Romney, his Republican opponent, last November to the female vote by 55pc to 44pc.
Mr Romney gained the male vote by 52pc to 45pc. The president stressed repeatedly on the campaign trail that the first bill he signed in the White House was the Lilly Ledbetter Fair Pay Act, which bans firms from paying women less than men for the same job.
Democrats ridiculed Mr Romney for claiming in a debate that he had drawn up "binders full of women" to fill senior positions in his administration while he was governor of Massachusetts.
Mr Romney and the Republicans were accused by senior Democrats of declaring war on women after pledging to restrict access to contraception and abortion.
In an unfortunate turn of events, the president made his remark about Miss Harris, California's most senior legal official, just as his wife, Michelle, mistakenly described herself as a "single mother" to a television interviewer.
Acknowledging that it was difficult for parents to find time to prepare good food, she said: "Believe me, as a busy single mother," before correcting herself to: "I shouldn't say single ... as a busy mother."
Attempting to make light of the misstatement, Mrs Obama added: "Sometimes, you know, when you've got the husband who's president, it can feel a little single. But he's there." (© Daily Telegraph, London)