He made his case in a speech to thousands in Hanoi, a day after meeting with Vietnamese leaders.
"Nations are more successful when universal rights are upheld," the president said, adding that countries prosper when they embrace freedom of expression, speech and assembly.
The president relayed the same message during a meeting with civil society groups. Obama said some activists were blocked from attending the meeting.
"There were several other activists who were invited that were prevented from coming," he said. "There are some folks who find it very difficult to assemble and organize peacefully around issues that they care deeply about."
The president didn't say who blocked the activists from attending, but did say this to Vietnam’s government:
"It's my hope that the government of Vietnam comes to recognize what we've recognized and what so many countries around the world have recognized, and that is that it's very hard to prosper in this modern economy if you haven't fully unleashed the potential of your people.”
Sitting next to Obama was singer and songwriter Mai Khoi, known as the "Lady Gaga of Vietnam."
She attempted to run in last week's National Assembly election, but was blocked from the ballot.
"I use my music to influence the people to raise awareness in democracy and human rights," she told ABC News before her meeting with the president.