The Dalai Lama and Dobriansky met in private at the University of Michigan after he wrapped up a weekend of lectures there.
They addressed reporters briefly before entering a room for discussions holding hands.
Dobriansky said the administration "has expressed its concern about the situation in Tibet and has urged restraint".
The 72-year-old Dalai Lama said he was surprised Dobriansky came to Michigan to see him during his US tour.
'Deep appreciation'
"I want to express my deep appreciation to your government, your president and state department and secretary of state and yourself [for] always showing genuine concern", he said.
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Demonstrations over Tibet have marred China's
lead-up to the Olympics in August [AFP] |
The meeting was criticised by China, which suggested that Washington was meddling in its internal affairs.
It was Dobriansky's 12th meeting with the Dalai Lama aimed at finding a way to resolve the Tibet issue amicably, the US state department said.
Beijing has accused the Dalai Lama of being behind the March 14 riots in Lhasa and the unrest that followed in other ethnic Tibetan areas, a charge he denies.
He says he wants autonomy for Tibet, not independence.
The Dalai Lama arrived in the US on April 10, a day after demonstrators disrupted the Olympic torch relay in San Francisco in protest over China's crackdown in Tibet.
Trading protests
Outside the University of Michigan's basketball arena where the Dalai Lama spoke on Sunday, several hundred pro-Chinese demonstrators held signs and waved Chinese flags.
The protest led to heated verbal exchanges between pro-Chinese and
pro-Tibetan demonstrators.
They traded shouts of "One China" with "Open the door! Let's see what's happening inside Tibet".
In another sign of the international fallout from China's crackdown on Tibetan protests, the European Commission's president has indicted he will discuss concerns over Tibet on a forthcoming visit to Beijing.
Jose Manuel Barroso, whose two-day China visit begins on Thursday, will take up the topic as part of discussions on human rights and freedom of expression, a spokesman for the European Union's executive body in Beijing said.
Barroso has said he opposes boycotting the Beijing Olympics over the Tibet issue.