One participant with the screen name Jeremy Taylor asked what Dung thought when sending his son to study in the US.
Responding Dung said the communist party and the government wanted to "leave the war behind to build up a good relationship with the US".
"Like many other Vietnamese citizens at that time, I had a strong hatred for the US government. But we do not hate the American people," he said.
Another person, with the screen name Pham Duong Quoc Tuan, asked why Dung had signed a decree "strictly banning privatisation of the press in any form".
"Doesn't it go against the goal of freedom and democracy that you are striving for?"
The government had recently decided to keep all 600 media outlets under state control.
Dung justified the decree as being "in line with Vietnamese law and in accordance with the aspirations of most of the people".
Another touchy subject Dung faced was the issue of seizures of land from farmers for development projects.
"What are your options to help people whose land was taken for infrastructure and development projects to keep them from being driven to poverty?" someone with the screen name Tran Van Toan from Ho Chi Minh City asked.
Dung explained that the seizures were "necessary to help move the country forward" and that the government was working on policies to "ensure that people will have a better life after the land was taken".
Many participants in the chat said they saw the first online dialogue by a senior Vietnamese official as a good way for the government to connect with the masses, and vice versa.
Previous Vietnamese leaders have taken a stiffer, more formal approach, typically reading speeches at events and avoiding questions from the international media.
Dung, who comes from south Vietnam, was appointed to the post of prime minister last June.