In a video of a private Clinton speech posted to YouTube yesterday, Clinton told a Canadian audience that she hoped the US would elect a woman to the White House because it would send "exactly the right historical signal" to men, women and children.
She said women in politics need to "dare to compete" and the nation needs to "take that leap of faith."
"Let me say this, hypothetically speaking, I really do hope that we have a woman president in my lifetime," Clinton said at a women's conference in Toronto on Thursday night.
The former secretary of state told the cheering audience that she would "certainly vote for the right woman to be president."
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Should she run for president in 2016, Clinton would emerge as the Democratic Party's leading contender to succeed President Barack Obama, but she has not said whether she will seek the White House again.
Clinton has said she is enjoying time off since departing the State Department in February but has taken a number of steps that could enhance a future presidential bid, speaking to a variety of groups around the country, working on a book and outlining her agenda at the foundation started by her husband, former President Bill Clinton.
The event was not open to the media, but a person in attendance posted a clip of Clinton's interview on YouTube yesterday.
Clinton spoke in an interview with Samantha Nutt, the founder and executive director of War Child Canada, a nonprofit that works with war-affected communities to help children.
The former first lady was asked if women lead differently than men and whether she thought the next US president would be a woman. Clinton cited former first lady Eleanor Roosevelt, who said that women in politics needed skin as "thick as a rhinoceros."
The former New York senator noted the US made history in 2008 by electing Obama, who defeated her in the Democratic primary on his way to becoming the nation's first black president.
"I hope that we will see a woman elected because I think it would send exactly the right historic signal to girls, women as well as boys and men. And I will certainly vote for the right woman to be president," Clinton said with a smile.