Zuckerberg said his plans include "road trips with Priscilla," referring to his wife, Priscilla Chan, who last year gave birth to a daughter, Max.
Destinations will include "stops in small towns and universities, visits to our offices across the country, meetings with teachers and scientists, and trips to fun places you recommend along the way".
Immediately, Zuckerberg faced scepticism.
"You went to Harvard; you have been removed - living in Silicon Valley - for a long time from the normal American[s]," wrote one Facebook user, Kinney Clausnitzer, in response.
"Please talk to working families that make under US$100k per year and you will get to hear the real truth of how things are out there... you won't get this from professors scientists and IT guys or college students."
Zuckerberg replied: "Yup, that's the plan," adding that he would post more "about how everyone around the world can join in".
Explaining his challenge in statesman-like language, the 32-year-old said the country was "at a turning point in history".
"For decades, technology and globalisation have made us more productive and connected. This has created many benefits, but for a lot of people it has also made life more challenging," he said.
"This has contributed to a greater sense of division than I have felt in my lifetime. We need to find a way to change the game so it works for everyone."
Last month, it emerged that Zuckerberg has sought to be allowed to serve two years in government without losing control of Facebook, according to court filings cited by Bloomberg.