By Kim Ghattas
BBC State Department correspondent, Washington
The issue of Aung San Suu Kyi was raised at the talks, Mr Campbell said
A top US official has confirmed that he has held a meeting with a Burmese minister in New York - the first such high-level talks in more than a decade.
Kurt Campbell, assistant US secretary of state for Asia, said he met Health Minister U Thaung on the margins of the UN General Assembly on Tuesday.
It came a day after the US announced a new policy on Burma, which consists of a mix of sanctions and dialogue.
Washington imposed sanctions on Burma in 1988.
But US Secretary of State Hillary Clinton said last week that neither sanctions nor isolation had worked on their own.
Kurt Campbell described his two-hour meeting with the Burmese minister as formal, careful and very respectful.
He said that he had made very clear to the Burmese what was expected of them for this new dialogue to continue.
At the top of the list were the issues of human rights and the treatment of opposition leader Aung San Suu Kyi.
Washington is also concerned about nuclear proliferation and ties with North Korea.
Mr Campbell said the new policy also had short-term goals such as exposing the next generation of officials to outside influence and improving humanitarian assistance for the Burmese.
Mr Campbell said the minister had presented him with a picture of encirclement and insurgencies, which informs the world view of the country's military leadership.
The US official said it was Burma that had made the first step towards dialogue, but he added it remained unclear precisely why.