The first US leader to visit the Asian nation said: "Our goal is to sustain the momentum."
Tens of thousands of people lined the streets of the capital, Rangoon, to see Mr Obama.
He shared words and a hug with Aung San Suu Kyi, the democracy activist who endured years of house arrest to gain freedom and become a politician.
"We are confident this support will continue through the difficult years that lie ahead," she said of the help from America, with Mr Obama at her side.
She added: "The most difficult time in any transition is when you think success is in sight. We have to be careful we're not lured by a mirage of success."
Mr Obama told her that if the nation's leaders keep making true reforms, "we will do everything we can to ensure success".
In a speech at the University of Rangoon, Mr Obama said: "Instead of being repressed, the right of people to assemble together must now be fully respected. Instead of being stifled, the veil of media censorship must continue to be lifted. As you take these steps, you can draw on your progress."
Long isolated due to a repressive military rule, Burma began a transition to democracy last year.
After meeting, President Thein Sein, who has orchestrated much of the transition to democracy, Mr Obama said the reforms could unleash "the incredible potential of this beautiful country".
Mr Obama met Ms Suu Kyi at the home where she spent years under house arrest.
The President's stop came between visits to Thailand and Cambodia.