Speaking in Singapore, he said women aren't perfect but are "indisputably better" than men.
He said most of the problems in the world came from old people, mostly men, holding onto positions of power.
He also spoke about political polarisation and the use of social media to spread falsehoods.
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Speaking at a private event on leadership, Mr Obama said while in office he had mused what a world run by women would look like.
"Now women, I just want you to know; you are not perfect, but what I can say pretty indisputably is that you're better than us [men].
"I'm absolutely confident that for two years if every nation on earth was run by women, you would see significant improvement across the board on just about everything... living standards and outcomes."
When asked if he would ever consider going back into political leadership, he said he believed in leaders stepping aside when the time came.
"If you look at the world and look at the problems it's usually old people, usually old men, not getting out of the way," he said.
"It is important for political leaders to try and remind themselves that you are there to do a job, but you are not there for life, you are not there in order to prop up your own sense of self-importance or your own power."
Mr Obama served as US president from 2009 until 2017.
Since leaving the White House, he and former first lady Michelle Obama have set up a foundation mentoring young leaders around the world.
The pair were in Kuala Lumpur last week for an Obama Foundation event.